KILLED
proof of input_YrFOYUvYOV.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# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished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), 282 ms]
        (12) CpxTypedWeightedCompleteTrs
        (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 7 ms]
        (14) CpxRNTS
        (15) InliningProof [UPPER BOUND(ID), 412 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), 0 ms]
        (22) CpxRNTS
(23) CpxTrsToCdtProof [UPPER BOUND(ID), 31 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), 8 ms]
    (30) CdtProblem
    (31) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (32) CdtProblem
    (33) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (34) CdtProblem
    (35) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (36) CdtProblem
    (37) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (38) CdtProblem
    (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (44) CdtProblem
    (45) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CdtProblem
    (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CdtProblem
    (65) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CdtProblem
    (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 37 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), 28 ms]
    (94) CdtProblem
    (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms]
    (98) CdtProblem
    (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms]
    (100) CdtProblem
    (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (102) CdtProblem
    (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 31 ms]
    (104) CdtProblem
    (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (106) CdtProblem
    (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms]
    (114) CdtProblem
    (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (116) CdtProblem
    (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 84 ms]
    (118) CdtProblem
    (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms]
    (122) CdtProblem
    (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (124) CdtProblem
    (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 20 ms]
    (126) CdtProblem
    (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms]
    (130) CdtProblem
    (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 66 ms]
    (134) CdtProblem
    (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CdtProblem
    (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms]
    (138) CdtProblem
    (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (140) CdtProblem
    (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 40 ms]
    (142) CdtProblem
    (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (144) CdtProblem
    (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 82 ms]
    (146) CdtProblem
    (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (148) CdtProblem
    (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 89 ms]
    (150) CdtProblem
    (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (152) CdtProblem
    (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 80 ms]
    (154) CdtProblem
    (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms]
    (156) CdtProblem
    (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 75 ms]
    (158) CdtProblem
    (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms]
    (160) CdtProblem
    (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 66 ms]
    (162) CdtProblem
    (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (164) CdtProblem
    (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms]
    (166) CdtProblem
    (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (168) CdtProblem
    (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms]
    (170) CdtProblem
    (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (172) CdtProblem
    (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms]
    (174) CdtProblem
    (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (176) CdtProblem
    (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms]
    (178) CdtProblem
    (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 25 ms]
    (180) CdtProblem
    (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms]
    (182) CdtProblem
    (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (184) CdtProblem
    (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 57 ms]
    (186) CdtProblem
    (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (188) CdtProblem
    (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 58 ms]
    (190) CdtProblem
    (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 15 ms]
    (192) CdtProblem
    (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 72 ms]
    (194) CdtProblem
    (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (196) CdtProblem
    (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms]
    (198) CdtProblem
    (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms]
    (200) CdtProblem
    (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms]
    (202) CdtProblem
    (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (204) 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__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2)
   a__U12(tt, V2) -> a__U13(a__isNat(V2))
   a__U13(tt) -> tt
   a__U21(tt, V1) -> a__U22(a__isNat(V1))
   a__U22(tt) -> tt
   a__U31(tt, N) -> mark(N)
   a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M)))
   a__and(tt, X) -> mark(X)
   a__isNat(0) -> tt
   a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2)
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2))
   a__isNatKind(s(V1)) -> a__isNatKind(V1)
   a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N)
   a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)
   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
   mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
   mark(isNat(X)) -> a__isNat(X)
   mark(U13(X)) -> a__U13(mark(X))
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
   mark(U22(X)) -> a__U22(mark(X))
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
   mark(and(X1, X2)) -> a__and(mark(X1), X2)
   mark(isNatKind(X)) -> a__isNatKind(X)
   mark(tt) -> tt
   mark(s(X)) -> s(mark(X))
   mark(0) -> 0
   a__U11(X1, X2, X3) -> U11(X1, X2, X3)
   a__U12(X1, X2) -> U12(X1, X2)
   a__isNat(X) -> isNat(X)
   a__U13(X) -> U13(X)
   a__U21(X1, X2) -> U21(X1, X2)
   a__U22(X) -> U22(X)
   a__U31(X1, X2) -> U31(X1, X2)
   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
   a__plus(X1, X2) -> plus(X1, X2)
   a__and(X1, X2) -> and(X1, X2)
   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__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2)
   a__U12(tt, V2) -> a__U13(a__isNat(V2))
   a__U13(tt) -> tt
   a__U21(tt, V1) -> a__U22(a__isNat(V1))
   a__U22(tt) -> tt
   a__U31(tt, N) -> mark(N)
   a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M)))
   a__and(tt, X) -> mark(X)
   a__isNat(0') -> tt
   a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2)
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
   a__isNatKind(0') -> tt
   a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2))
   a__isNatKind(s(V1)) -> a__isNatKind(V1)
   a__plus(N, 0') -> a__U31(a__and(a__isNat(N), isNatKind(N)), N)
   a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)
   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
   mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
   mark(isNat(X)) -> a__isNat(X)
   mark(U13(X)) -> a__U13(mark(X))
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
   mark(U22(X)) -> a__U22(mark(X))
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
   mark(and(X1, X2)) -> a__and(mark(X1), X2)
   mark(isNatKind(X)) -> a__isNatKind(X)
   mark(tt) -> tt
   mark(s(X)) -> s(mark(X))
   mark(0') -> 0'
   a__U11(X1, X2, X3) -> U11(X1, X2, X3)
   a__U12(X1, X2) -> U12(X1, X2)
   a__isNat(X) -> isNat(X)
   a__U13(X) -> U13(X)
   a__U21(X1, X2) -> U21(X1, X2)
   a__U22(X) -> U22(X)
   a__U31(X1, X2) -> U31(X1, X2)
   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
   a__plus(X1, X2) -> plus(X1, X2)
   a__and(X1, X2) -> and(X1, X2)
   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__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2)
   a__U12(tt, V2) -> a__U13(a__isNat(V2))
   a__U13(tt) -> tt
   a__U21(tt, V1) -> a__U22(a__isNat(V1))
   a__U22(tt) -> tt
   a__U31(tt, N) -> mark(N)
   a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M)))
   a__and(tt, X) -> mark(X)
   a__isNat(0) -> tt
   a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2)
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2))
   a__isNatKind(s(V1)) -> a__isNatKind(V1)
   a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N)
   a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)
   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
   mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
   mark(isNat(X)) -> a__isNat(X)
   mark(U13(X)) -> a__U13(mark(X))
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
   mark(U22(X)) -> a__U22(mark(X))
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
   mark(and(X1, X2)) -> a__and(mark(X1), X2)
   mark(isNatKind(X)) -> a__isNatKind(X)
   mark(tt) -> tt
   mark(s(X)) -> s(mark(X))
   mark(0) -> 0
   a__U11(X1, X2, X3) -> U11(X1, X2, X3)
   a__U12(X1, X2) -> U12(X1, X2)
   a__isNat(X) -> isNat(X)
   a__U13(X) -> U13(X)
   a__U21(X1, X2) -> U21(X1, X2)
   a__U22(X) -> U22(X)
   a__U31(X1, X2) -> U31(X1, X2)
   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
   a__plus(X1, X2) -> plus(X1, X2)
   a__and(X1, X2) -> and(X1, X2)
   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__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) [1]
   a__U12(tt, V2) -> a__U13(a__isNat(V2)) [1]
   a__U13(tt) -> tt [1]
   a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1]
   a__U22(tt) -> tt [1]
   a__U31(tt, N) -> mark(N) [1]
   a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) [1]
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1]
   a__isNatKind(0) -> tt [1]
   a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) [1]
   a__isNatKind(s(V1)) -> a__isNatKind(V1) [1]
   a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) [1]
   a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [1]
   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1]
   mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U13(X)) -> a__U13(mark(X)) [1]
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1]
   mark(U22(X)) -> a__U22(mark(X)) [1]
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), X2) [1]
   mark(isNatKind(X)) -> a__isNatKind(X) [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(0) -> 0 [1]
   a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1]
   a__U12(X1, X2) -> U12(X1, X2) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U13(X) -> U13(X) [1]
   a__U21(X1, X2) -> U21(X1, X2) [1]
   a__U22(X) -> U22(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [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__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) [1]
   a__U12(tt, V2) -> a__U13(a__isNat(V2)) [1]
   a__U13(tt) -> tt [1]
   a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1]
   a__U22(tt) -> tt [1]
   a__U31(tt, N) -> mark(N) [1]
   a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) [1]
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1]
   a__isNatKind(0) -> tt [1]
   a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) [1]
   a__isNatKind(s(V1)) -> a__isNatKind(V1) [1]
   a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) [1]
   a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [1]
   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1]
   mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U13(X)) -> a__U13(mark(X)) [1]
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1]
   mark(U22(X)) -> a__U22(mark(X)) [1]
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), X2) [1]
   mark(isNatKind(X)) -> a__isNatKind(X) [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(0) -> 0 [1]
   a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1]
   a__U12(X1, X2) -> U12(X1, X2) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U13(X) -> U13(X) [1]
   a__U21(X1, X2) -> U21(X1, X2) [1]
   a__U22(X) -> U22(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNatKind(X) -> isNatKind(X) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
tt :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
mark :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
s :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
0 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41

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__isNatKind_1
   a__and_2
   a__isNat_1
   a__U22_1
   a__U11_3
   a__U41_3
   a__U31_2
   a__U12_2
   a__U21_2
   a__U13_1
   a__plus_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__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) [1]
   a__U12(tt, V2) -> a__U13(a__isNat(V2)) [1]
   a__U13(tt) -> tt [1]
   a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1]
   a__U22(tt) -> tt [1]
   a__U31(tt, N) -> mark(N) [1]
   a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) [1]
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1]
   a__isNatKind(0) -> tt [1]
   a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) [1]
   a__isNatKind(s(V1)) -> a__isNatKind(V1) [1]
   a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) [1]
   a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [1]
   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1]
   mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U13(X)) -> a__U13(mark(X)) [1]
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1]
   mark(U22(X)) -> a__U22(mark(X)) [1]
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), X2) [1]
   mark(isNatKind(X)) -> a__isNatKind(X) [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(0) -> 0 [1]
   a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1]
   a__U12(X1, X2) -> U12(X1, X2) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U13(X) -> U13(X) [1]
   a__U21(X1, X2) -> U21(X1, X2) [1]
   a__U22(X) -> U22(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNatKind(X) -> isNatKind(X) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
tt :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
mark :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
s :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
0 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41

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__U11(tt, 0, V2) -> a__U12(tt, V2) [2]
   a__U11(tt, plus(V1', V2'), V2) -> a__U12(a__U11(a__and(a__isNatKind(V1'), isNatKind(V2')), V1', V2'), V2) [2]
   a__U11(tt, s(V1''), V2) -> a__U12(a__U21(a__isNatKind(V1''), V1''), V2) [2]
   a__U11(tt, V1, V2) -> a__U12(isNat(V1), V2) [2]
   a__U12(tt, 0) -> a__U13(tt) [2]
   a__U12(tt, plus(V11, V2'')) -> a__U13(a__U11(a__and(a__isNatKind(V11), isNatKind(V2'')), V11, V2'')) [2]
   a__U12(tt, s(V12)) -> a__U13(a__U21(a__isNatKind(V12), V12)) [2]
   a__U12(tt, V2) -> a__U13(isNat(V2)) [2]
   a__U13(tt) -> tt [1]
   a__U21(tt, 0) -> a__U22(tt) [2]
   a__U21(tt, plus(V13, V21)) -> a__U22(a__U11(a__and(a__isNatKind(V13), isNatKind(V21)), V13, V21)) [2]
   a__U21(tt, s(V14)) -> a__U22(a__U21(a__isNatKind(V14), V14)) [2]
   a__U21(tt, V1) -> a__U22(isNat(V1)) [2]
   a__U22(tt) -> tt [1]
   a__U31(tt, N) -> mark(N) [1]
   a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(0, V2)) -> a__U11(a__and(tt, isNatKind(V2)), 0, V2) [2]
   a__isNat(plus(plus(V15, V22), V2)) -> a__U11(a__and(a__and(a__isNatKind(V15), isNatKind(V22)), isNatKind(V2)), plus(V15, V22), V2) [2]
   a__isNat(plus(s(V16), V2)) -> a__U11(a__and(a__isNatKind(V16), isNatKind(V2)), s(V16), V2) [2]
   a__isNat(plus(V1, V2)) -> a__U11(a__and(isNatKind(V1), isNatKind(V2)), V1, V2) [2]
   a__isNat(s(0)) -> a__U21(tt, 0) [2]
   a__isNat(s(plus(V17, V23))) -> a__U21(a__and(a__isNatKind(V17), isNatKind(V23)), plus(V17, V23)) [2]
   a__isNat(s(s(V18))) -> a__U21(a__isNatKind(V18), s(V18)) [2]
   a__isNat(s(V1)) -> a__U21(isNatKind(V1), V1) [2]
   a__isNatKind(0) -> tt [1]
   a__isNatKind(plus(0, V2)) -> a__and(tt, isNatKind(V2)) [2]
   a__isNatKind(plus(plus(V19, V24), V2)) -> a__and(a__and(a__isNatKind(V19), isNatKind(V24)), isNatKind(V2)) [2]
   a__isNatKind(plus(s(V110), V2)) -> a__and(a__isNatKind(V110), isNatKind(V2)) [2]
   a__isNatKind(plus(V1, V2)) -> a__and(isNatKind(V1), isNatKind(V2)) [2]
   a__isNatKind(s(V1)) -> a__isNatKind(V1) [1]
   a__plus(0, 0) -> a__U31(a__and(tt, isNatKind(0)), 0) [2]
   a__plus(plus(V111, V25), 0) -> a__U31(a__and(a__U11(a__and(a__isNatKind(V111), isNatKind(V25)), V111, V25), isNatKind(plus(V111, V25))), plus(V111, V25)) [2]
   a__plus(s(V112), 0) -> a__U31(a__and(a__U21(a__isNatKind(V112), V112), isNatKind(s(V112))), s(V112)) [2]
   a__plus(N, 0) -> a__U31(a__and(isNat(N), isNatKind(N)), N) [2]
   a__plus(N, s(0)) -> a__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(N), isNatKind(N))), 0, N) [2]
   a__plus(N, s(plus(V113, V26))) -> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(V113), isNatKind(V26)), V113, V26), isNatKind(plus(V113, V26))), and(isNat(N), isNatKind(N))), plus(V113, V26), N) [2]
   a__plus(N, s(s(V114))) -> a__U41(a__and(a__and(a__U21(a__isNatKind(V114), V114), isNatKind(s(V114))), and(isNat(N), isNatKind(N))), s(V114), N) [2]
   a__plus(N, s(M)) -> a__U41(a__and(a__and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [2]
   mark(U11(U11(X1104, X2104, X333), X2, X3)) -> a__U11(a__U11(mark(X1104), X2104, X333), X2, X3) [2]
   mark(U11(U12(X1105, X2105), X2, X3)) -> a__U11(a__U12(mark(X1105), X2105), X2, X3) [2]
   mark(U11(isNat(X100), X2, X3)) -> a__U11(a__isNat(X100), X2, X3) [2]
   mark(U11(U13(X101), X2, X3)) -> a__U11(a__U13(mark(X101)), X2, X3) [2]
   mark(U11(U21(X1106, X2106), X2, X3)) -> a__U11(a__U21(mark(X1106), X2106), X2, X3) [2]
   mark(U11(U22(X102), X2, X3)) -> a__U11(a__U22(mark(X102)), X2, X3) [2]
   mark(U11(U31(X1107, X2107), X2, X3)) -> a__U11(a__U31(mark(X1107), X2107), X2, X3) [2]
   mark(U11(U41(X1108, X2108, X334), X2, X3)) -> a__U11(a__U41(mark(X1108), X2108, X334), X2, X3) [2]
   mark(U11(plus(X1109, X2109), X2, X3)) -> a__U11(a__plus(mark(X1109), mark(X2109)), X2, X3) [2]
   mark(U11(and(X1110, X2110), X2, X3)) -> a__U11(a__and(mark(X1110), X2110), X2, X3) [2]
   mark(U11(isNatKind(X103), X2, X3)) -> a__U11(a__isNatKind(X103), X2, X3) [2]
   mark(U11(tt, X2, X3)) -> a__U11(tt, X2, X3) [2]
   mark(U11(s(X104), X2, X3)) -> a__U11(s(mark(X104)), X2, X3) [2]
   mark(U11(0, X2, X3)) -> a__U11(0, X2, X3) [2]
   mark(U12(U11(X1111, X2111, X335), X2)) -> a__U12(a__U11(mark(X1111), X2111, X335), X2) [2]
   mark(U12(U12(X1112, X2112), X2)) -> a__U12(a__U12(mark(X1112), X2112), X2) [2]
   mark(U12(isNat(X105), X2)) -> a__U12(a__isNat(X105), X2) [2]
   mark(U12(U13(X106), X2)) -> a__U12(a__U13(mark(X106)), X2) [2]
   mark(U12(U21(X1113, X2113), X2)) -> a__U12(a__U21(mark(X1113), X2113), X2) [2]
   mark(U12(U22(X107), X2)) -> a__U12(a__U22(mark(X107)), X2) [2]
   mark(U12(U31(X1114, X2114), X2)) -> a__U12(a__U31(mark(X1114), X2114), X2) [2]
   mark(U12(U41(X1115, X2115, X336), X2)) -> a__U12(a__U41(mark(X1115), X2115, X336), X2) [2]
   mark(U12(plus(X1116, X2116), X2)) -> a__U12(a__plus(mark(X1116), mark(X2116)), X2) [2]
   mark(U12(and(X1117, X2117), X2)) -> a__U12(a__and(mark(X1117), X2117), X2) [2]
   mark(U12(isNatKind(X108), X2)) -> a__U12(a__isNatKind(X108), X2) [2]
   mark(U12(tt, X2)) -> a__U12(tt, X2) [2]
   mark(U12(s(X109), X2)) -> a__U12(s(mark(X109)), X2) [2]
   mark(U12(0, X2)) -> a__U12(0, X2) [2]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U13(U11(X1118, X2118, X337))) -> a__U13(a__U11(mark(X1118), X2118, X337)) [2]
   mark(U13(U12(X1119, X2119))) -> a__U13(a__U12(mark(X1119), X2119)) [2]
   mark(U13(isNat(X200))) -> a__U13(a__isNat(X200)) [2]
   mark(U13(U13(X201))) -> a__U13(a__U13(mark(X201))) [2]
   mark(U13(U21(X1120, X2120))) -> a__U13(a__U21(mark(X1120), X2120)) [2]
   mark(U13(U22(X202))) -> a__U13(a__U22(mark(X202))) [2]
   mark(U13(U31(X1121, X2121))) -> a__U13(a__U31(mark(X1121), X2121)) [2]
   mark(U13(U41(X1122, X2122, X338))) -> a__U13(a__U41(mark(X1122), X2122, X338)) [2]
   mark(U13(plus(X1123, X2123))) -> a__U13(a__plus(mark(X1123), mark(X2123))) [2]
   mark(U13(and(X1124, X2124))) -> a__U13(a__and(mark(X1124), X2124)) [2]
   mark(U13(isNatKind(X203))) -> a__U13(a__isNatKind(X203)) [2]
   mark(U13(tt)) -> a__U13(tt) [2]
   mark(U13(s(X204))) -> a__U13(s(mark(X204))) [2]
   mark(U13(0)) -> a__U13(0) [2]
   mark(U21(U11(X1125, X2125, X339), X2)) -> a__U21(a__U11(mark(X1125), X2125, X339), X2) [2]
   mark(U21(U12(X1126, X2126), X2)) -> a__U21(a__U12(mark(X1126), X2126), X2) [2]
   mark(U21(isNat(X205), X2)) -> a__U21(a__isNat(X205), X2) [2]
   mark(U21(U13(X206), X2)) -> a__U21(a__U13(mark(X206)), X2) [2]
   mark(U21(U21(X1127, X2127), X2)) -> a__U21(a__U21(mark(X1127), X2127), X2) [2]
   mark(U21(U22(X207), X2)) -> a__U21(a__U22(mark(X207)), X2) [2]
   mark(U21(U31(X1128, X2128), X2)) -> a__U21(a__U31(mark(X1128), X2128), X2) [2]
   mark(U21(U41(X1129, X2129, X340), X2)) -> a__U21(a__U41(mark(X1129), X2129, X340), X2) [2]
   mark(U21(plus(X1130, X2130), X2)) -> a__U21(a__plus(mark(X1130), mark(X2130)), X2) [2]
   mark(U21(and(X1131, X2131), X2)) -> a__U21(a__and(mark(X1131), X2131), X2) [2]
   mark(U21(isNatKind(X208), X2)) -> a__U21(a__isNatKind(X208), X2) [2]
   mark(U21(tt, X2)) -> a__U21(tt, X2) [2]
   mark(U21(s(X209), X2)) -> a__U21(s(mark(X209)), X2) [2]
   mark(U21(0, X2)) -> a__U21(0, X2) [2]
   mark(U22(U11(X1132, X2132, X341))) -> a__U22(a__U11(mark(X1132), X2132, X341)) [2]
   mark(U22(U12(X1133, X2133))) -> a__U22(a__U12(mark(X1133), X2133)) [2]
   mark(U22(isNat(X300))) -> a__U22(a__isNat(X300)) [2]
   mark(U22(U13(X301))) -> a__U22(a__U13(mark(X301))) [2]
   mark(U22(U21(X1134, X2134))) -> a__U22(a__U21(mark(X1134), X2134)) [2]
   mark(U22(U22(X302))) -> a__U22(a__U22(mark(X302))) [2]
   mark(U22(U31(X1135, X2135))) -> a__U22(a__U31(mark(X1135), X2135)) [2]
   mark(U22(U41(X1136, X2136, X342))) -> a__U22(a__U41(mark(X1136), X2136, X342)) [2]
   mark(U22(plus(X1137, X2137))) -> a__U22(a__plus(mark(X1137), mark(X2137))) [2]
   mark(U22(and(X1138, X2138))) -> a__U22(a__and(mark(X1138), X2138)) [2]
   mark(U22(isNatKind(X303))) -> a__U22(a__isNatKind(X303)) [2]
   mark(U22(tt)) -> a__U22(tt) [2]
   mark(U22(s(X304))) -> a__U22(s(mark(X304))) [2]
   mark(U22(0)) -> a__U22(0) [2]
   mark(U31(U11(X1139, X2139, X343), X2)) -> a__U31(a__U11(mark(X1139), X2139, X343), X2) [2]
   mark(U31(U12(X1140, X2140), X2)) -> a__U31(a__U12(mark(X1140), X2140), X2) [2]
   mark(U31(isNat(X305), X2)) -> a__U31(a__isNat(X305), X2) [2]
   mark(U31(U13(X306), X2)) -> a__U31(a__U13(mark(X306)), X2) [2]
   mark(U31(U21(X1141, X2141), X2)) -> a__U31(a__U21(mark(X1141), X2141), X2) [2]
   mark(U31(U22(X307), X2)) -> a__U31(a__U22(mark(X307)), X2) [2]
   mark(U31(U31(X1142, X2142), X2)) -> a__U31(a__U31(mark(X1142), X2142), X2) [2]
   mark(U31(U41(X1143, X2143, X344), X2)) -> a__U31(a__U41(mark(X1143), X2143, X344), X2) [2]
   mark(U31(plus(X1144, X2144), X2)) -> a__U31(a__plus(mark(X1144), mark(X2144)), X2) [2]
   mark(U31(and(X1145, X2145), X2)) -> a__U31(a__and(mark(X1145), X2145), X2) [2]
   mark(U31(isNatKind(X308), X2)) -> a__U31(a__isNatKind(X308), X2) [2]
   mark(U31(tt, X2)) -> a__U31(tt, X2) [2]
   mark(U31(s(X309), X2)) -> a__U31(s(mark(X309)), X2) [2]
   mark(U31(0, X2)) -> a__U31(0, X2) [2]
   mark(U41(U11(X1146, X2146, X345), X2, X3)) -> a__U41(a__U11(mark(X1146), X2146, X345), X2, X3) [2]
   mark(U41(U12(X1147, X2147), X2, X3)) -> a__U41(a__U12(mark(X1147), X2147), X2, X3) [2]
   mark(U41(isNat(X346), X2, X3)) -> a__U41(a__isNat(X346), X2, X3) [2]
   mark(U41(U13(X347), X2, X3)) -> a__U41(a__U13(mark(X347)), X2, X3) [2]
   mark(U41(U21(X1148, X2148), X2, X3)) -> a__U41(a__U21(mark(X1148), X2148), X2, X3) [2]
   mark(U41(U22(X348), X2, X3)) -> a__U41(a__U22(mark(X348)), X2, X3) [2]
   mark(U41(U31(X1149, X2149), X2, X3)) -> a__U41(a__U31(mark(X1149), X2149), X2, X3) [2]
   mark(U41(U41(X1150, X2150, X349), X2, X3)) -> a__U41(a__U41(mark(X1150), X2150, X349), X2, X3) [2]
   mark(U41(plus(X1151, X2151), X2, X3)) -> a__U41(a__plus(mark(X1151), mark(X2151)), X2, X3) [2]
   mark(U41(and(X1152, X2152), X2, X3)) -> a__U41(a__and(mark(X1152), X2152), X2, X3) [2]
   mark(U41(isNatKind(X350), X2, X3)) -> a__U41(a__isNatKind(X350), X2, X3) [2]
   mark(U41(tt, X2, X3)) -> a__U41(tt, X2, X3) [2]
   mark(U41(s(X351), X2, X3)) -> a__U41(s(mark(X351)), X2, X3) [2]
   mark(U41(0, X2, X3)) -> a__U41(0, X2, X3) [2]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(and(U11(X1258, X2258, X3116), X2)) -> a__and(a__U11(mark(X1258), X2258, X3116), X2) [2]
   mark(and(U12(X1259, X2259), X2)) -> a__and(a__U12(mark(X1259), X2259), X2) [2]
   mark(and(isNat(X441), X2)) -> a__and(a__isNat(X441), X2) [2]
   mark(and(U13(X442), X2)) -> a__and(a__U13(mark(X442)), X2) [2]
   mark(and(U21(X1260, X2260), X2)) -> a__and(a__U21(mark(X1260), X2260), X2) [2]
   mark(and(U22(X443), X2)) -> a__and(a__U22(mark(X443)), X2) [2]
   mark(and(U31(X1261, X2261), X2)) -> a__and(a__U31(mark(X1261), X2261), X2) [2]
   mark(and(U41(X1262, X2262, X3117), X2)) -> a__and(a__U41(mark(X1262), X2262, X3117), X2) [2]
   mark(and(plus(X1263, X2263), X2)) -> a__and(a__plus(mark(X1263), mark(X2263)), X2) [2]
   mark(and(and(X1264, X2264), X2)) -> a__and(a__and(mark(X1264), X2264), X2) [2]
   mark(and(isNatKind(X444), X2)) -> a__and(a__isNatKind(X444), X2) [2]
   mark(and(tt, X2)) -> a__and(tt, X2) [2]
   mark(and(s(X445), X2)) -> a__and(s(mark(X445)), X2) [2]
   mark(and(0, X2)) -> a__and(0, X2) [2]
   mark(isNatKind(X)) -> a__isNatKind(X) [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(0) -> 0 [1]
   a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1]
   a__U12(X1, X2) -> U12(X1, X2) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U13(X) -> U13(X) [1]
   a__U21(X1, X2) -> U21(X1, X2) [1]
   a__U22(X) -> U22(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNatKind(X) -> isNatKind(X) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
tt :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
mark :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
s :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
0 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41

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:

   tt => 1
   0 => 0

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

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

   a__U11(z, z', z'') -{ 2 }-> a__U12(a__U21(a__isNatKind(V1''), V1''), V2) :|: V1'' >= 0, z = 1, z' = 1 + V1'', V2 >= 0, z'' = V2
   a__U11(z, z', z'') -{ 2 }-> a__U12(a__U11(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2'), V2) :|: z = 1, z' = 1 + V1' + V2', V2 >= 0, z'' = V2, V2' >= 0, V1' >= 0
   a__U11(z, z', z'') -{ 2 }-> a__U12(1, V2) :|: z = 1, V2 >= 0, z'' = V2, z' = 0
   a__U11(z, z', z'') -{ 2 }-> a__U12(1 + V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1
   a__U11(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U12(z, z') -{ 2 }-> a__U13(a__U21(a__isNatKind(V12), V12)) :|: z = 1, V12 >= 0, z' = 1 + V12
   a__U12(z, z') -{ 2 }-> a__U13(a__U11(a__and(a__isNatKind(V11), 1 + V2''), V11, V2'')) :|: V11 >= 0, V2'' >= 0, z = 1, z' = 1 + V11 + V2''
   a__U12(z, z') -{ 2 }-> a__U13(1) :|: z = 1, z' = 0
   a__U12(z, z') -{ 2 }-> a__U13(1 + V2) :|: z' = V2, z = 1, V2 >= 0
   a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U13(z) -{ 1 }-> 1 :|: z = 1
   a__U13(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(V14), V14)) :|: V14 >= 0, z = 1, z' = 1 + V14
   a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: V21 >= 0, V13 >= 0, z = 1, z' = 1 + V13 + V21
   a__U21(z, z') -{ 2 }-> a__U22(1) :|: z = 1, z' = 0
   a__U21(z, z') -{ 2 }-> a__U22(1 + V1) :|: V1 >= 0, z = 1, z' = V1
   a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U22(z) -{ 1 }-> 1 :|: z = 1
   a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U31(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0
   a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U41(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__and(z, z') -{ 1 }-> mark(X) :|: z' = X, z = 1, 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(V18), 1 + V18) :|: V18 >= 0, z = 1 + (1 + V18)
   a__isNat(z) -{ 2 }-> a__U21(a__and(a__isNatKind(V17), 1 + V23), 1 + V17 + V23) :|: V23 >= 0, z = 1 + (1 + V17 + V23), V17 >= 0
   a__isNat(z) -{ 2 }-> a__U21(1, 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(V16), 1 + V2), 1 + V16, V2) :|: V16 >= 0, V2 >= 0, z = 1 + (1 + V16) + V2
   a__isNat(z) -{ 2 }-> a__U11(a__and(a__and(a__isNatKind(V15), 1 + V22), 1 + V2), 1 + V15 + V22, V2) :|: V22 >= 0, V2 >= 0, V15 >= 0, z = 1 + (1 + V15 + V22) + V2
   a__isNat(z) -{ 2 }-> a__U11(a__and(1, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNat(z) -{ 2 }-> a__U11(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNat(z) -{ 1 }-> 1 :|: z = 0
   a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatKind(z) -{ 1 }-> a__isNatKind(V1) :|: z = 1 + V1, V1 >= 0
   a__isNatKind(z) -{ 2 }-> a__and(a__isNatKind(V110), 1 + V2) :|: V110 >= 0, V2 >= 0, z = 1 + (1 + V110) + V2
   a__isNatKind(z) -{ 2 }-> a__and(a__and(a__isNatKind(V19), 1 + V24), 1 + V2) :|: V24 >= 0, V19 >= 0, z = 1 + (1 + V19 + V24) + V2, V2 >= 0
   a__isNatKind(z) -{ 2 }-> a__and(1, 1 + V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNatKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatKind(z) -{ 1 }-> 1 :|: z = 0
   a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U21(a__isNatKind(V114), V114), 1 + (1 + V114)), 1 + (1 + N) + (1 + N)), 1 + V114, N) :|: V114 >= 0, z' = 1 + (1 + V114), z = N, N >= 0
   a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(V113), 1 + V26), V113, V26), 1 + (1 + V113 + V26)), 1 + (1 + N) + (1 + N)), 1 + V113 + V26, N) :|: z = N, z' = 1 + (1 + V113 + V26), N >= 0, V113 >= 0, V26 >= 0
   a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1, 1 + 0), 1 + (1 + N) + (1 + N)), 0, N) :|: z = N, z' = 1 + 0, N >= 0
   a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1 + M, 1 + M), 1 + (1 + N) + (1 + N)), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U21(a__isNatKind(V112), V112), 1 + (1 + V112)), 1 + V112) :|: z = 1 + V112, V112 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U11(a__and(a__isNatKind(V111), 1 + V25), V111, V25), 1 + (1 + V111 + V25)), 1 + V111 + V25) :|: z = 1 + V111 + V25, V25 >= 0, V111 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(a__and(1, 1 + 0), 0) :|: z = 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(a__and(1 + N, 1 + N), N) :|: z = N, z' = 0, N >= 0
   a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 2 }-> a__and(a__plus(mark(X1263), mark(X2263)), X2) :|: X1263 >= 0, z = 1 + (1 + X1263 + X2263) + X2, X2 >= 0, X2263 >= 0
   mark(z) -{ 2 }-> a__and(a__isNatKind(X444), X2) :|: z = 1 + (1 + X444) + X2, X444 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__isNat(X441), X2) :|: z = 1 + (1 + X441) + X2, X441 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__and(mark(X1264), X2264), X2) :|: X2264 >= 0, z = 1 + (1 + X1264 + X2264) + X2, X1264 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U41(mark(X1262), X2262, X3117), X2) :|: X1262 >= 0, X3117 >= 0, X2262 >= 0, X2 >= 0, z = 1 + (1 + X1262 + X2262 + X3117) + X2
   mark(z) -{ 2 }-> a__and(a__U31(mark(X1261), X2261), X2) :|: z = 1 + (1 + X1261 + X2261) + X2, X2261 >= 0, X2 >= 0, X1261 >= 0
   mark(z) -{ 2 }-> a__and(a__U22(mark(X443)), X2) :|: z = 1 + (1 + X443) + X2, X443 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U21(mark(X1260), X2260), X2) :|: z = 1 + (1 + X1260 + X2260) + X2, X2260 >= 0, X1260 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U13(mark(X442)), X2) :|: X442 >= 0, z = 1 + (1 + X442) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U12(mark(X1259), X2259), X2) :|: X2259 >= 0, X2 >= 0, z = 1 + (1 + X1259 + X2259) + X2, X1259 >= 0
   mark(z) -{ 2 }-> a__and(a__U11(mark(X1258), X2258, X3116), X2) :|: z = 1 + (1 + X1258 + X2258 + X3116) + X2, X2258 >= 0, X3116 >= 0, X2 >= 0, X1258 >= 0
   mark(z) -{ 2 }-> a__and(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__and(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__and(1 + mark(X445), X2) :|: z = 1 + (1 + X445) + X2, X2 >= 0, X445 >= 0
   mark(z) -{ 2 }-> a__U41(a__plus(mark(X1151), mark(X2151)), X2, X3) :|: X2151 >= 0, X3 >= 0, X1151 >= 0, z = 1 + (1 + X1151 + X2151) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__isNatKind(X350), X2, X3) :|: X350 >= 0, z = 1 + (1 + X350) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__isNat(X346), X2, X3) :|: X3 >= 0, z = 1 + (1 + X346) + X2 + X3, X346 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__and(mark(X1152), X2152), X2, X3) :|: z = 1 + (1 + X1152 + X2152) + X2 + X3, X2152 >= 0, X3 >= 0, X2 >= 0, X1152 >= 0
   mark(z) -{ 2 }-> a__U41(a__U41(mark(X1150), X2150, X349), X2, X3) :|: X2150 >= 0, z = 1 + (1 + X1150 + X2150 + X349) + X2 + X3, X3 >= 0, X349 >= 0, X1150 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U31(mark(X1149), X2149), X2, X3) :|: z = 1 + (1 + X1149 + X2149) + X2 + X3, X2149 >= 0, X3 >= 0, X2 >= 0, X1149 >= 0
   mark(z) -{ 2 }-> a__U41(a__U22(mark(X348)), X2, X3) :|: z = 1 + (1 + X348) + X2 + X3, X3 >= 0, X348 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U21(mark(X1148), X2148), X2, X3) :|: X2148 >= 0, z = 1 + (1 + X1148 + X2148) + X2 + X3, X3 >= 0, X1148 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U13(mark(X347)), X2, X3) :|: X347 >= 0, z = 1 + (1 + X347) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U12(mark(X1147), X2147), X2, X3) :|: X1147 >= 0, X3 >= 0, X2147 >= 0, X2 >= 0, z = 1 + (1 + X1147 + X2147) + X2 + X3
   mark(z) -{ 2 }-> a__U41(a__U11(mark(X1146), X2146, X345), X2, X3) :|: z = 1 + (1 + X1146 + X2146 + X345) + X2 + X3, X1146 >= 0, X345 >= 0, X3 >= 0, X2146 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(1 + mark(X351), X2, X3) :|: z = 1 + (1 + X351) + X2 + X3, X3 >= 0, X351 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__plus(mark(X1144), mark(X2144)), X2) :|: X2144 >= 0, z = 1 + (1 + X1144 + X2144) + X2, X1144 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__isNatKind(X308), X2) :|: z = 1 + (1 + X308) + X2, X308 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__isNat(X305), X2) :|: X305 >= 0, z = 1 + (1 + X305) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__and(mark(X1145), X2145), X2) :|: z = 1 + (1 + X1145 + X2145) + X2, X1145 >= 0, X2 >= 0, X2145 >= 0
   mark(z) -{ 2 }-> a__U31(a__U41(mark(X1143), X2143, X344), X2) :|: X344 >= 0, z = 1 + (1 + X1143 + X2143 + X344) + X2, X2143 >= 0, X2 >= 0, X1143 >= 0
   mark(z) -{ 2 }-> a__U31(a__U31(mark(X1142), X2142), X2) :|: z = 1 + (1 + X1142 + X2142) + X2, X2142 >= 0, X2 >= 0, X1142 >= 0
   mark(z) -{ 2 }-> a__U31(a__U22(mark(X307)), X2) :|: z = 1 + (1 + X307) + X2, X307 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U21(mark(X1141), X2141), X2) :|: X2141 >= 0, z = 1 + (1 + X1141 + X2141) + X2, X2 >= 0, X1141 >= 0
   mark(z) -{ 2 }-> a__U31(a__U13(mark(X306)), X2) :|: z = 1 + (1 + X306) + X2, X306 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U12(mark(X1140), X2140), X2) :|: X2140 >= 0, z = 1 + (1 + X1140 + X2140) + X2, X1140 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U11(mark(X1139), X2139, X343), X2) :|: X343 >= 0, X2139 >= 0, z = 1 + (1 + X1139 + X2139 + X343) + X2, X2 >= 0, X1139 >= 0
   mark(z) -{ 2 }-> a__U31(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(1 + mark(X309), X2) :|: X309 >= 0, z = 1 + (1 + X309) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U22(a__plus(mark(X1137), mark(X2137))) :|: X2137 >= 0, X1137 >= 0, z = 1 + (1 + X1137 + X2137)
   mark(z) -{ 2 }-> a__U22(a__isNatKind(X303)) :|: z = 1 + (1 + X303), X303 >= 0
   mark(z) -{ 2 }-> a__U22(a__isNat(X300)) :|: X300 >= 0, z = 1 + (1 + X300)
   mark(z) -{ 2 }-> a__U22(a__and(mark(X1138), X2138)) :|: X2138 >= 0, z = 1 + (1 + X1138 + X2138), X1138 >= 0
   mark(z) -{ 2 }-> a__U22(a__U41(mark(X1136), X2136, X342)) :|: z = 1 + (1 + X1136 + X2136 + X342), X342 >= 0, X1136 >= 0, X2136 >= 0
   mark(z) -{ 2 }-> a__U22(a__U31(mark(X1135), X2135)) :|: X1135 >= 0, z = 1 + (1 + X1135 + X2135), X2135 >= 0
   mark(z) -{ 2 }-> a__U22(a__U22(mark(X302))) :|: X302 >= 0, z = 1 + (1 + X302)
   mark(z) -{ 2 }-> a__U22(a__U21(mark(X1134), X2134)) :|: X2134 >= 0, z = 1 + (1 + X1134 + X2134), X1134 >= 0
   mark(z) -{ 2 }-> a__U22(a__U13(mark(X301))) :|: X301 >= 0, z = 1 + (1 + X301)
   mark(z) -{ 2 }-> a__U22(a__U12(mark(X1133), X2133)) :|: z = 1 + (1 + X1133 + X2133), X2133 >= 0, X1133 >= 0
   mark(z) -{ 2 }-> a__U22(a__U11(mark(X1132), X2132, X341)) :|: z = 1 + (1 + X1132 + X2132 + X341), X341 >= 0, X2132 >= 0, X1132 >= 0
   mark(z) -{ 2 }-> a__U22(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__U22(0) :|: z = 1 + 0
   mark(z) -{ 2 }-> a__U22(1 + mark(X304)) :|: z = 1 + (1 + X304), X304 >= 0
   mark(z) -{ 2 }-> a__U21(a__plus(mark(X1130), mark(X2130)), X2) :|: X2130 >= 0, X1130 >= 0, z = 1 + (1 + X1130 + X2130) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__isNatKind(X208), X2) :|: z = 1 + (1 + X208) + X2, X208 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__isNat(X205), X2) :|: X205 >= 0, z = 1 + (1 + X205) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__and(mark(X1131), X2131), X2) :|: z = 1 + (1 + X1131 + X2131) + X2, X2131 >= 0, X2 >= 0, X1131 >= 0
   mark(z) -{ 2 }-> a__U21(a__U41(mark(X1129), X2129, X340), X2) :|: X1129 >= 0, z = 1 + (1 + X1129 + X2129 + X340) + X2, X2129 >= 0, X340 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U31(mark(X1128), X2128), X2) :|: z = 1 + (1 + X1128 + X2128) + X2, X2128 >= 0, X1128 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U22(mark(X207)), X2) :|: z = 1 + (1 + X207) + X2, X207 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U21(mark(X1127), X2127), X2) :|: z = 1 + (1 + X1127 + X2127) + X2, X2127 >= 0, X1127 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U13(mark(X206)), X2) :|: X206 >= 0, z = 1 + (1 + X206) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U12(mark(X1126), X2126), X2) :|: z = 1 + (1 + X1126 + X2126) + X2, X1126 >= 0, X2 >= 0, X2126 >= 0
   mark(z) -{ 2 }-> a__U21(a__U11(mark(X1125), X2125, X339), X2) :|: X1125 >= 0, X339 >= 0, z = 1 + (1 + X1125 + X2125 + X339) + X2, X2 >= 0, X2125 >= 0
   mark(z) -{ 2 }-> a__U21(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U21(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U21(1 + mark(X209), X2) :|: z = 1 + (1 + X209) + X2, X209 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U13(a__plus(mark(X1123), mark(X2123))) :|: X2123 >= 0, X1123 >= 0, z = 1 + (1 + X1123 + X2123)
   mark(z) -{ 2 }-> a__U13(a__isNatKind(X203)) :|: z = 1 + (1 + X203), X203 >= 0
   mark(z) -{ 2 }-> a__U13(a__isNat(X200)) :|: z = 1 + (1 + X200), X200 >= 0
   mark(z) -{ 2 }-> a__U13(a__and(mark(X1124), X2124)) :|: X1124 >= 0, z = 1 + (1 + X1124 + X2124), X2124 >= 0
   mark(z) -{ 2 }-> a__U13(a__U41(mark(X1122), X2122, X338)) :|: X2122 >= 0, X338 >= 0, z = 1 + (1 + X1122 + X2122 + X338), X1122 >= 0
   mark(z) -{ 2 }-> a__U13(a__U31(mark(X1121), X2121)) :|: X1121 >= 0, z = 1 + (1 + X1121 + X2121), X2121 >= 0
   mark(z) -{ 2 }-> a__U13(a__U22(mark(X202))) :|: X202 >= 0, z = 1 + (1 + X202)
   mark(z) -{ 2 }-> a__U13(a__U21(mark(X1120), X2120)) :|: z = 1 + (1 + X1120 + X2120), X2120 >= 0, X1120 >= 0
   mark(z) -{ 2 }-> a__U13(a__U13(mark(X201))) :|: X201 >= 0, z = 1 + (1 + X201)
   mark(z) -{ 2 }-> a__U13(a__U12(mark(X1119), X2119)) :|: z = 1 + (1 + X1119 + X2119), X1119 >= 0, X2119 >= 0
   mark(z) -{ 2 }-> a__U13(a__U11(mark(X1118), X2118, X337)) :|: z = 1 + (1 + X1118 + X2118 + X337), X1118 >= 0, X2118 >= 0, X337 >= 0
   mark(z) -{ 2 }-> a__U13(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__U13(0) :|: z = 1 + 0
   mark(z) -{ 2 }-> a__U13(1 + mark(X204)) :|: z = 1 + (1 + X204), X204 >= 0
   mark(z) -{ 2 }-> a__U12(a__plus(mark(X1116), mark(X2116)), X2) :|: z = 1 + (1 + X1116 + X2116) + X2, X1116 >= 0, X2 >= 0, X2116 >= 0
   mark(z) -{ 2 }-> a__U12(a__isNatKind(X108), X2) :|: z = 1 + (1 + X108) + X2, X2 >= 0, X108 >= 0
   mark(z) -{ 2 }-> a__U12(a__isNat(X105), X2) :|: X105 >= 0, z = 1 + (1 + X105) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__and(mark(X1117), X2117), X2) :|: X2117 >= 0, z = 1 + (1 + X1117 + X2117) + X2, X1117 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U41(mark(X1115), X2115, X336), X2) :|: z = 1 + (1 + X1115 + X2115 + X336) + X2, X1115 >= 0, X2 >= 0, X336 >= 0, X2115 >= 0
   mark(z) -{ 2 }-> a__U12(a__U31(mark(X1114), X2114), X2) :|: X1114 >= 0, z = 1 + (1 + X1114 + X2114) + X2, X2 >= 0, X2114 >= 0
   mark(z) -{ 2 }-> a__U12(a__U22(mark(X107)), X2) :|: X107 >= 0, z = 1 + (1 + X107) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U21(mark(X1113), X2113), X2) :|: z = 1 + (1 + X1113 + X2113) + X2, X2113 >= 0, X1113 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U13(mark(X106)), X2) :|: X106 >= 0, z = 1 + (1 + X106) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U12(mark(X1112), X2112), X2) :|: z = 1 + (1 + X1112 + X2112) + X2, X2112 >= 0, X2 >= 0, X1112 >= 0
   mark(z) -{ 2 }-> a__U12(a__U11(mark(X1111), X2111, X335), X2) :|: X1111 >= 0, z = 1 + (1 + X1111 + X2111 + X335) + X2, X2111 >= 0, X335 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U12(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U12(1 + mark(X109), X2) :|: X2 >= 0, z = 1 + (1 + X109) + X2, X109 >= 0
   mark(z) -{ 2 }-> a__U11(a__plus(mark(X1109), mark(X2109)), X2, X3) :|: z = 1 + (1 + X1109 + X2109) + X2 + X3, X2109 >= 0, X3 >= 0, X2 >= 0, X1109 >= 0
   mark(z) -{ 2 }-> a__U11(a__isNatKind(X103), X2, X3) :|: X103 >= 0, z = 1 + (1 + X103) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__isNat(X100), X2, X3) :|: z = 1 + (1 + X100) + X2 + X3, X3 >= 0, X2 >= 0, X100 >= 0
   mark(z) -{ 2 }-> a__U11(a__and(mark(X1110), X2110), X2, X3) :|: X1110 >= 0, X2110 >= 0, z = 1 + (1 + X1110 + X2110) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U41(mark(X1108), X2108, X334), X2, X3) :|: X1108 >= 0, z = 1 + (1 + X1108 + X2108 + X334) + X2 + X3, X3 >= 0, X2108 >= 0, X334 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U31(mark(X1107), X2107), X2, X3) :|: X2107 >= 0, X1107 >= 0, z = 1 + (1 + X1107 + X2107) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U22(mark(X102)), X2, X3) :|: z = 1 + (1 + X102) + X2 + X3, X3 >= 0, X2 >= 0, X102 >= 0
   mark(z) -{ 2 }-> a__U11(a__U21(mark(X1106), X2106), X2, X3) :|: X2106 >= 0, z = 1 + (1 + X1106 + X2106) + X2 + X3, X1106 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U13(mark(X101)), X2, X3) :|: X3 >= 0, X2 >= 0, z = 1 + (1 + X101) + X2 + X3, X101 >= 0
   mark(z) -{ 2 }-> a__U11(a__U12(mark(X1105), X2105), X2, X3) :|: z = 1 + (1 + X1105 + X2105) + X2 + X3, X1105 >= 0, X3 >= 0, X2 >= 0, X2105 >= 0
   mark(z) -{ 2 }-> a__U11(a__U11(mark(X1104), X2104, X333), X2, X3) :|: X1104 >= 0, X333 >= 0, z = 1 + (1 + X1104 + X2104 + X333) + X2 + X3, X3 >= 0, X2104 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(1 + mark(X104), X2, X3) :|: X104 >= 0, X3 >= 0, z = 1 + (1 + X104) + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0


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

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

   a__U13(z) -{ 1 }-> 1 :|: z = 1
   a__U13(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U22(z) -{ 1 }-> 1 :|: z = 1

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

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

   a__U11(z, z', z'') -{ 2 }-> a__U12(a__U21(a__isNatKind(V1''), V1''), V2) :|: V1'' >= 0, z = 1, z' = 1 + V1'', V2 >= 0, z'' = V2
   a__U11(z, z', z'') -{ 2 }-> a__U12(a__U11(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2'), V2) :|: z = 1, z' = 1 + V1' + V2', V2 >= 0, z'' = V2, V2' >= 0, V1' >= 0
   a__U11(z, z', z'') -{ 2 }-> a__U12(1, V2) :|: z = 1, V2 >= 0, z'' = V2, z' = 0
   a__U11(z, z', z'') -{ 2 }-> a__U12(1 + V1, V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1
   a__U11(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U12(z, z') -{ 2 }-> a__U13(a__U21(a__isNatKind(V12), V12)) :|: z = 1, V12 >= 0, z' = 1 + V12
   a__U12(z, z') -{ 2 }-> a__U13(a__U11(a__and(a__isNatKind(V11), 1 + V2''), V11, V2'')) :|: V11 >= 0, V2'' >= 0, z = 1, z' = 1 + V11 + V2''
   a__U12(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1
   a__U12(z, z') -{ 3 }-> 1 :|: z' = V2, z = 1, V2 >= 0, 1 + V2 = 1
   a__U12(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X
   a__U12(z, z') -{ 3 }-> 1 + X :|: z' = V2, z = 1, V2 >= 0, X >= 0, 1 + V2 = X
   a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U13(z) -{ 1 }-> 1 :|: z = 1
   a__U13(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(V14), V14)) :|: V14 >= 0, z = 1, z' = 1 + V14
   a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: V21 >= 0, V13 >= 0, z = 1, z' = 1 + V13 + V21
   a__U21(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1
   a__U21(z, z') -{ 3 }-> 1 :|: V1 >= 0, z = 1, z' = V1, 1 + V1 = 1
   a__U21(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X
   a__U21(z, z') -{ 3 }-> 1 + X :|: V1 >= 0, z = 1, 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 }-> 1 :|: z = 1
   a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U31(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0
   a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U41(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__and(z, z') -{ 1 }-> mark(X) :|: z' = X, z = 1, 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(V18), 1 + V18) :|: V18 >= 0, z = 1 + (1 + V18)
   a__isNat(z) -{ 2 }-> a__U21(a__and(a__isNatKind(V17), 1 + V23), 1 + V17 + V23) :|: V23 >= 0, z = 1 + (1 + V17 + V23), V17 >= 0
   a__isNat(z) -{ 2 }-> a__U21(1, 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(V16), 1 + V2), 1 + V16, V2) :|: V16 >= 0, V2 >= 0, z = 1 + (1 + V16) + V2
   a__isNat(z) -{ 2 }-> a__U11(a__and(a__and(a__isNatKind(V15), 1 + V22), 1 + V2), 1 + V15 + V22, V2) :|: V22 >= 0, V2 >= 0, V15 >= 0, z = 1 + (1 + V15 + V22) + V2
   a__isNat(z) -{ 2 }-> a__U11(a__and(1, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNat(z) -{ 2 }-> a__U11(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNat(z) -{ 1 }-> 1 :|: z = 0
   a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatKind(z) -{ 1 }-> a__isNatKind(V1) :|: z = 1 + V1, V1 >= 0
   a__isNatKind(z) -{ 2 }-> a__and(a__isNatKind(V110), 1 + V2) :|: V110 >= 0, V2 >= 0, z = 1 + (1 + V110) + V2
   a__isNatKind(z) -{ 2 }-> a__and(a__and(a__isNatKind(V19), 1 + V24), 1 + V2) :|: V24 >= 0, V19 >= 0, z = 1 + (1 + V19 + V24) + V2, V2 >= 0
   a__isNatKind(z) -{ 2 }-> a__and(1, 1 + V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNatKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatKind(z) -{ 1 }-> 1 :|: z = 0
   a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U21(a__isNatKind(V114), V114), 1 + (1 + V114)), 1 + (1 + N) + (1 + N)), 1 + V114, N) :|: V114 >= 0, z' = 1 + (1 + V114), z = N, N >= 0
   a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(V113), 1 + V26), V113, V26), 1 + (1 + V113 + V26)), 1 + (1 + N) + (1 + N)), 1 + V113 + V26, N) :|: z = N, z' = 1 + (1 + V113 + V26), N >= 0, V113 >= 0, V26 >= 0
   a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1, 1 + 0), 1 + (1 + N) + (1 + N)), 0, N) :|: z = N, z' = 1 + 0, N >= 0
   a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1 + M, 1 + M), 1 + (1 + N) + (1 + N)), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U21(a__isNatKind(V112), V112), 1 + (1 + V112)), 1 + V112) :|: z = 1 + V112, V112 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U11(a__and(a__isNatKind(V111), 1 + V25), V111, V25), 1 + (1 + V111 + V25)), 1 + V111 + V25) :|: z = 1 + V111 + V25, V25 >= 0, V111 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(a__and(1, 1 + 0), 0) :|: z = 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(a__and(1 + N, 1 + N), N) :|: z = N, z' = 0, N >= 0
   a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 2 }-> a__and(a__plus(mark(X1263), mark(X2263)), X2) :|: X1263 >= 0, z = 1 + (1 + X1263 + X2263) + X2, X2 >= 0, X2263 >= 0
   mark(z) -{ 2 }-> a__and(a__isNatKind(X444), X2) :|: z = 1 + (1 + X444) + X2, X444 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__isNat(X441), X2) :|: z = 1 + (1 + X441) + X2, X441 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__and(mark(X1264), X2264), X2) :|: X2264 >= 0, z = 1 + (1 + X1264 + X2264) + X2, X1264 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U41(mark(X1262), X2262, X3117), X2) :|: X1262 >= 0, X3117 >= 0, X2262 >= 0, X2 >= 0, z = 1 + (1 + X1262 + X2262 + X3117) + X2
   mark(z) -{ 2 }-> a__and(a__U31(mark(X1261), X2261), X2) :|: z = 1 + (1 + X1261 + X2261) + X2, X2261 >= 0, X2 >= 0, X1261 >= 0
   mark(z) -{ 2 }-> a__and(a__U22(mark(X443)), X2) :|: z = 1 + (1 + X443) + X2, X443 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U21(mark(X1260), X2260), X2) :|: z = 1 + (1 + X1260 + X2260) + X2, X2260 >= 0, X1260 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U13(mark(X442)), X2) :|: X442 >= 0, z = 1 + (1 + X442) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U12(mark(X1259), X2259), X2) :|: X2259 >= 0, X2 >= 0, z = 1 + (1 + X1259 + X2259) + X2, X1259 >= 0
   mark(z) -{ 2 }-> a__and(a__U11(mark(X1258), X2258, X3116), X2) :|: z = 1 + (1 + X1258 + X2258 + X3116) + X2, X2258 >= 0, X3116 >= 0, X2 >= 0, X1258 >= 0
   mark(z) -{ 2 }-> a__and(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__and(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__and(1 + mark(X445), X2) :|: z = 1 + (1 + X445) + X2, X2 >= 0, X445 >= 0
   mark(z) -{ 2 }-> a__U41(a__plus(mark(X1151), mark(X2151)), X2, X3) :|: X2151 >= 0, X3 >= 0, X1151 >= 0, z = 1 + (1 + X1151 + X2151) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__isNatKind(X350), X2, X3) :|: X350 >= 0, z = 1 + (1 + X350) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__isNat(X346), X2, X3) :|: X3 >= 0, z = 1 + (1 + X346) + X2 + X3, X346 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__and(mark(X1152), X2152), X2, X3) :|: z = 1 + (1 + X1152 + X2152) + X2 + X3, X2152 >= 0, X3 >= 0, X2 >= 0, X1152 >= 0
   mark(z) -{ 2 }-> a__U41(a__U41(mark(X1150), X2150, X349), X2, X3) :|: X2150 >= 0, z = 1 + (1 + X1150 + X2150 + X349) + X2 + X3, X3 >= 0, X349 >= 0, X1150 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U31(mark(X1149), X2149), X2, X3) :|: z = 1 + (1 + X1149 + X2149) + X2 + X3, X2149 >= 0, X3 >= 0, X2 >= 0, X1149 >= 0
   mark(z) -{ 2 }-> a__U41(a__U22(mark(X348)), X2, X3) :|: z = 1 + (1 + X348) + X2 + X3, X3 >= 0, X348 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U21(mark(X1148), X2148), X2, X3) :|: X2148 >= 0, z = 1 + (1 + X1148 + X2148) + X2 + X3, X3 >= 0, X1148 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U13(mark(X347)), X2, X3) :|: X347 >= 0, z = 1 + (1 + X347) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U12(mark(X1147), X2147), X2, X3) :|: X1147 >= 0, X3 >= 0, X2147 >= 0, X2 >= 0, z = 1 + (1 + X1147 + X2147) + X2 + X3
   mark(z) -{ 2 }-> a__U41(a__U11(mark(X1146), X2146, X345), X2, X3) :|: z = 1 + (1 + X1146 + X2146 + X345) + X2 + X3, X1146 >= 0, X345 >= 0, X3 >= 0, X2146 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(1 + mark(X351), X2, X3) :|: z = 1 + (1 + X351) + X2 + X3, X3 >= 0, X351 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__plus(mark(X1144), mark(X2144)), X2) :|: X2144 >= 0, z = 1 + (1 + X1144 + X2144) + X2, X1144 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__isNatKind(X308), X2) :|: z = 1 + (1 + X308) + X2, X308 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__isNat(X305), X2) :|: X305 >= 0, z = 1 + (1 + X305) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__and(mark(X1145), X2145), X2) :|: z = 1 + (1 + X1145 + X2145) + X2, X1145 >= 0, X2 >= 0, X2145 >= 0
   mark(z) -{ 2 }-> a__U31(a__U41(mark(X1143), X2143, X344), X2) :|: X344 >= 0, z = 1 + (1 + X1143 + X2143 + X344) + X2, X2143 >= 0, X2 >= 0, X1143 >= 0
   mark(z) -{ 2 }-> a__U31(a__U31(mark(X1142), X2142), X2) :|: z = 1 + (1 + X1142 + X2142) + X2, X2142 >= 0, X2 >= 0, X1142 >= 0
   mark(z) -{ 2 }-> a__U31(a__U22(mark(X307)), X2) :|: z = 1 + (1 + X307) + X2, X307 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U21(mark(X1141), X2141), X2) :|: X2141 >= 0, z = 1 + (1 + X1141 + X2141) + X2, X2 >= 0, X1141 >= 0
   mark(z) -{ 2 }-> a__U31(a__U13(mark(X306)), X2) :|: z = 1 + (1 + X306) + X2, X306 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U12(mark(X1140), X2140), X2) :|: X2140 >= 0, z = 1 + (1 + X1140 + X2140) + X2, X1140 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U11(mark(X1139), X2139, X343), X2) :|: X343 >= 0, X2139 >= 0, z = 1 + (1 + X1139 + X2139 + X343) + X2, X2 >= 0, X1139 >= 0
   mark(z) -{ 2 }-> a__U31(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(1 + mark(X309), X2) :|: X309 >= 0, z = 1 + (1 + X309) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U22(a__plus(mark(X1137), mark(X2137))) :|: X2137 >= 0, X1137 >= 0, z = 1 + (1 + X1137 + X2137)
   mark(z) -{ 2 }-> a__U22(a__isNatKind(X303)) :|: z = 1 + (1 + X303), X303 >= 0
   mark(z) -{ 2 }-> a__U22(a__isNat(X300)) :|: X300 >= 0, z = 1 + (1 + X300)
   mark(z) -{ 2 }-> a__U22(a__and(mark(X1138), X2138)) :|: X2138 >= 0, z = 1 + (1 + X1138 + X2138), X1138 >= 0
   mark(z) -{ 2 }-> a__U22(a__U41(mark(X1136), X2136, X342)) :|: z = 1 + (1 + X1136 + X2136 + X342), X342 >= 0, X1136 >= 0, X2136 >= 0
   mark(z) -{ 2 }-> a__U22(a__U31(mark(X1135), X2135)) :|: X1135 >= 0, z = 1 + (1 + X1135 + X2135), X2135 >= 0
   mark(z) -{ 2 }-> a__U22(a__U22(mark(X302))) :|: X302 >= 0, z = 1 + (1 + X302)
   mark(z) -{ 2 }-> a__U22(a__U21(mark(X1134), X2134)) :|: X2134 >= 0, z = 1 + (1 + X1134 + X2134), X1134 >= 0
   mark(z) -{ 2 }-> a__U22(a__U13(mark(X301))) :|: X301 >= 0, z = 1 + (1 + X301)
   mark(z) -{ 2 }-> a__U22(a__U12(mark(X1133), X2133)) :|: z = 1 + (1 + X1133 + X2133), X2133 >= 0, X1133 >= 0
   mark(z) -{ 2 }-> a__U22(a__U11(mark(X1132), X2132, X341)) :|: z = 1 + (1 + X1132 + X2132 + X341), X341 >= 0, X2132 >= 0, X1132 >= 0
   mark(z) -{ 2 }-> a__U22(1 + mark(X304)) :|: z = 1 + (1 + X304), X304 >= 0
   mark(z) -{ 2 }-> a__U21(a__plus(mark(X1130), mark(X2130)), X2) :|: X2130 >= 0, X1130 >= 0, z = 1 + (1 + X1130 + X2130) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__isNatKind(X208), X2) :|: z = 1 + (1 + X208) + X2, X208 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__isNat(X205), X2) :|: X205 >= 0, z = 1 + (1 + X205) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__and(mark(X1131), X2131), X2) :|: z = 1 + (1 + X1131 + X2131) + X2, X2131 >= 0, X2 >= 0, X1131 >= 0
   mark(z) -{ 2 }-> a__U21(a__U41(mark(X1129), X2129, X340), X2) :|: X1129 >= 0, z = 1 + (1 + X1129 + X2129 + X340) + X2, X2129 >= 0, X340 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U31(mark(X1128), X2128), X2) :|: z = 1 + (1 + X1128 + X2128) + X2, X2128 >= 0, X1128 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U22(mark(X207)), X2) :|: z = 1 + (1 + X207) + X2, X207 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U21(mark(X1127), X2127), X2) :|: z = 1 + (1 + X1127 + X2127) + X2, X2127 >= 0, X1127 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U13(mark(X206)), X2) :|: X206 >= 0, z = 1 + (1 + X206) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U12(mark(X1126), X2126), X2) :|: z = 1 + (1 + X1126 + X2126) + X2, X1126 >= 0, X2 >= 0, X2126 >= 0
   mark(z) -{ 2 }-> a__U21(a__U11(mark(X1125), X2125, X339), X2) :|: X1125 >= 0, X339 >= 0, z = 1 + (1 + X1125 + X2125 + X339) + X2, X2 >= 0, X2125 >= 0
   mark(z) -{ 2 }-> a__U21(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U21(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U21(1 + mark(X209), X2) :|: z = 1 + (1 + X209) + X2, X209 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U13(a__plus(mark(X1123), mark(X2123))) :|: X2123 >= 0, X1123 >= 0, z = 1 + (1 + X1123 + X2123)
   mark(z) -{ 2 }-> a__U13(a__isNatKind(X203)) :|: z = 1 + (1 + X203), X203 >= 0
   mark(z) -{ 2 }-> a__U13(a__isNat(X200)) :|: z = 1 + (1 + X200), X200 >= 0
   mark(z) -{ 2 }-> a__U13(a__and(mark(X1124), X2124)) :|: X1124 >= 0, z = 1 + (1 + X1124 + X2124), X2124 >= 0
   mark(z) -{ 2 }-> a__U13(a__U41(mark(X1122), X2122, X338)) :|: X2122 >= 0, X338 >= 0, z = 1 + (1 + X1122 + X2122 + X338), X1122 >= 0
   mark(z) -{ 2 }-> a__U13(a__U31(mark(X1121), X2121)) :|: X1121 >= 0, z = 1 + (1 + X1121 + X2121), X2121 >= 0
   mark(z) -{ 2 }-> a__U13(a__U22(mark(X202))) :|: X202 >= 0, z = 1 + (1 + X202)
   mark(z) -{ 2 }-> a__U13(a__U21(mark(X1120), X2120)) :|: z = 1 + (1 + X1120 + X2120), X2120 >= 0, X1120 >= 0
   mark(z) -{ 2 }-> a__U13(a__U13(mark(X201))) :|: X201 >= 0, z = 1 + (1 + X201)
   mark(z) -{ 2 }-> a__U13(a__U12(mark(X1119), X2119)) :|: z = 1 + (1 + X1119 + X2119), X1119 >= 0, X2119 >= 0
   mark(z) -{ 2 }-> a__U13(a__U11(mark(X1118), X2118, X337)) :|: z = 1 + (1 + X1118 + X2118 + X337), X1118 >= 0, X2118 >= 0, X337 >= 0
   mark(z) -{ 2 }-> a__U13(1 + mark(X204)) :|: z = 1 + (1 + X204), X204 >= 0
   mark(z) -{ 2 }-> a__U12(a__plus(mark(X1116), mark(X2116)), X2) :|: z = 1 + (1 + X1116 + X2116) + X2, X1116 >= 0, X2 >= 0, X2116 >= 0
   mark(z) -{ 2 }-> a__U12(a__isNatKind(X108), X2) :|: z = 1 + (1 + X108) + X2, X2 >= 0, X108 >= 0
   mark(z) -{ 2 }-> a__U12(a__isNat(X105), X2) :|: X105 >= 0, z = 1 + (1 + X105) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__and(mark(X1117), X2117), X2) :|: X2117 >= 0, z = 1 + (1 + X1117 + X2117) + X2, X1117 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U41(mark(X1115), X2115, X336), X2) :|: z = 1 + (1 + X1115 + X2115 + X336) + X2, X1115 >= 0, X2 >= 0, X336 >= 0, X2115 >= 0
   mark(z) -{ 2 }-> a__U12(a__U31(mark(X1114), X2114), X2) :|: X1114 >= 0, z = 1 + (1 + X1114 + X2114) + X2, X2 >= 0, X2114 >= 0
   mark(z) -{ 2 }-> a__U12(a__U22(mark(X107)), X2) :|: X107 >= 0, z = 1 + (1 + X107) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U21(mark(X1113), X2113), X2) :|: z = 1 + (1 + X1113 + X2113) + X2, X2113 >= 0, X1113 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U13(mark(X106)), X2) :|: X106 >= 0, z = 1 + (1 + X106) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U12(mark(X1112), X2112), X2) :|: z = 1 + (1 + X1112 + X2112) + X2, X2112 >= 0, X2 >= 0, X1112 >= 0
   mark(z) -{ 2 }-> a__U12(a__U11(mark(X1111), X2111, X335), X2) :|: X1111 >= 0, z = 1 + (1 + X1111 + X2111 + X335) + X2, X2111 >= 0, X335 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U12(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U12(1 + mark(X109), X2) :|: X2 >= 0, z = 1 + (1 + X109) + X2, X109 >= 0
   mark(z) -{ 2 }-> a__U11(a__plus(mark(X1109), mark(X2109)), X2, X3) :|: z = 1 + (1 + X1109 + X2109) + X2 + X3, X2109 >= 0, X3 >= 0, X2 >= 0, X1109 >= 0
   mark(z) -{ 2 }-> a__U11(a__isNatKind(X103), X2, X3) :|: X103 >= 0, z = 1 + (1 + X103) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__isNat(X100), X2, X3) :|: z = 1 + (1 + X100) + X2 + X3, X3 >= 0, X2 >= 0, X100 >= 0
   mark(z) -{ 2 }-> a__U11(a__and(mark(X1110), X2110), X2, X3) :|: X1110 >= 0, X2110 >= 0, z = 1 + (1 + X1110 + X2110) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U41(mark(X1108), X2108, X334), X2, X3) :|: X1108 >= 0, z = 1 + (1 + X1108 + X2108 + X334) + X2 + X3, X3 >= 0, X2108 >= 0, X334 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U31(mark(X1107), X2107), X2, X3) :|: X2107 >= 0, X1107 >= 0, z = 1 + (1 + X1107 + X2107) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U22(mark(X102)), X2, X3) :|: z = 1 + (1 + X102) + X2 + X3, X3 >= 0, X2 >= 0, X102 >= 0
   mark(z) -{ 2 }-> a__U11(a__U21(mark(X1106), X2106), X2, X3) :|: X2106 >= 0, z = 1 + (1 + X1106 + X2106) + X2 + X3, X1106 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U13(mark(X101)), X2, X3) :|: X3 >= 0, X2 >= 0, z = 1 + (1 + X101) + X2 + X3, X101 >= 0
   mark(z) -{ 2 }-> a__U11(a__U12(mark(X1105), X2105), X2, X3) :|: z = 1 + (1 + X1105 + X2105) + X2 + X3, X1105 >= 0, X3 >= 0, X2 >= 0, X2105 >= 0
   mark(z) -{ 2 }-> a__U11(a__U11(mark(X1104), X2104, X333), X2, X3) :|: X1104 >= 0, X333 >= 0, z = 1 + (1 + X1104 + X2104 + X333) + X2 + X3, X3 >= 0, X2104 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(1 + mark(X104), X2, X3) :|: X104 >= 0, X3 >= 0, z = 1 + (1 + X104) + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 3 }-> 1 :|: z = 1 + 1, 1 = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0


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(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', z'') -{ 2 }-> a__U12(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z' - 1 >= 0, z = 1, z'' >= 0
   a__U11(z, z', z'') -{ 2 }-> a__U12(a__U11(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2'), z'') :|: z = 1, z' = 1 + V1' + V2', z'' >= 0, V2' >= 0, V1' >= 0
   a__U11(z, z', z'') -{ 2 }-> a__U12(1, z'') :|: z = 1, z'' >= 0, z' = 0
   a__U11(z, z', z'') -{ 2 }-> a__U12(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   a__U11(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   a__U12(z, z') -{ 2 }-> a__U13(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z = 1, z' - 1 >= 0
   a__U12(z, z') -{ 2 }-> a__U13(a__U11(a__and(a__isNatKind(V11), 1 + V2''), V11, V2'')) :|: V11 >= 0, V2'' >= 0, z = 1, z' = 1 + V11 + V2''
   a__U12(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1
   a__U12(z, z') -{ 3 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1
   a__U12(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X
   a__U12(z, z') -{ 3 }-> 1 + X :|: z = 1, z' >= 0, X >= 0, 1 + z' = X
   a__U12(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__U13(z) -{ 1 }-> 1 :|: z = 1
   a__U13(z) -{ 1 }-> 1 + z :|: z >= 0
   a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z' - 1 >= 0, z = 1
   a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: V21 >= 0, V13 >= 0, z = 1, z' = 1 + V13 + V21
   a__U21(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1
   a__U21(z, z') -{ 3 }-> 1 :|: z' >= 0, z = 1, 1 + z' = 1
   a__U21(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X
   a__U21(z, z') -{ 3 }-> 1 + X :|: z' >= 0, z = 1, X >= 0, 1 + z' = X
   a__U21(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__U22(z) -{ 1 }-> 1 :|: z = 1
   a__U22(z) -{ 1 }-> 1 + z :|: z >= 0
   a__U31(z, z') -{ 1 }-> mark(z') :|: z = 1, z' >= 0
   a__U31(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__U41(z, z', z'') -{ 1 }-> 1 + a__plus(mark(z''), mark(z')) :|: z = 1, z' >= 0, z'' >= 0
   a__U41(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   a__and(z, z') -{ 1 }-> mark(z') :|: z = 1, 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__and(a__isNatKind(V17), 1 + V23), 1 + V17 + V23) :|: V23 >= 0, z = 1 + (1 + V17 + V23), V17 >= 0
   a__isNat(z) -{ 2 }-> a__U21(1, 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(V16), 1 + V2), 1 + V16, V2) :|: V16 >= 0, V2 >= 0, z = 1 + (1 + V16) + V2
   a__isNat(z) -{ 2 }-> a__U11(a__and(a__and(a__isNatKind(V15), 1 + V22), 1 + V2), 1 + V15 + V22, V2) :|: V22 >= 0, V2 >= 0, V15 >= 0, z = 1 + (1 + V15 + V22) + V2
   a__isNat(z) -{ 2 }-> a__U11(a__and(1, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0
   a__isNat(z) -{ 2 }-> a__U11(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNat(z) -{ 1 }-> 1 :|: z = 0
   a__isNat(z) -{ 1 }-> 1 + z :|: z >= 0
   a__isNatKind(z) -{ 1 }-> a__isNatKind(z - 1) :|: z - 1 >= 0
   a__isNatKind(z) -{ 2 }-> a__and(a__isNatKind(V110), 1 + V2) :|: V110 >= 0, V2 >= 0, z = 1 + (1 + V110) + V2
   a__isNatKind(z) -{ 2 }-> a__and(a__and(a__isNatKind(V19), 1 + V24), 1 + V2) :|: V24 >= 0, V19 >= 0, z = 1 + (1 + V19 + V24) + V2, V2 >= 0
   a__isNatKind(z) -{ 2 }-> a__and(1, 1 + (z - 1)) :|: z - 1 >= 0
   a__isNatKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatKind(z) -{ 1 }-> 1 :|: z = 0
   a__isNatKind(z) -{ 1 }-> 1 + z :|: z >= 0
   a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U21(a__isNatKind(z' - 2), z' - 2), 1 + (1 + (z' - 2))), 1 + (1 + z) + (1 + z)), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0
   a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(a__U11(a__and(a__isNatKind(V113), 1 + V26), V113, V26), 1 + (1 + V113 + V26)), 1 + (1 + z) + (1 + z)), 1 + V113 + V26, z) :|: z' = 1 + (1 + V113 + V26), z >= 0, V113 >= 0, V26 >= 0
   a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1, 1 + 0), 1 + (1 + z) + (1 + z)), 0, z) :|: z' = 1 + 0, z >= 0
   a__plus(z, z') -{ 2 }-> a__U41(a__and(a__and(1 + (z' - 1), 1 + (z' - 1)), 1 + (1 + z) + (1 + z)), z' - 1, z) :|: z' - 1 >= 0, z >= 0
   a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U21(a__isNatKind(z - 1), z - 1), 1 + (1 + (z - 1))), 1 + (z - 1)) :|: z - 1 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(a__and(a__U11(a__and(a__isNatKind(V111), 1 + V25), V111, V25), 1 + (1 + V111 + V25)), 1 + V111 + V25) :|: z = 1 + V111 + V25, V25 >= 0, V111 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(a__and(1, 1 + 0), 0) :|: z = 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(a__and(1 + z, 1 + z), z) :|: z' = 0, z >= 0
   a__plus(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__isNatKind(z - 1) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__isNat(z - 1) :|: z - 1 >= 0
   mark(z) -{ 2 }-> a__and(a__plus(mark(X1263), mark(X2263)), X2) :|: X1263 >= 0, z = 1 + (1 + X1263 + X2263) + X2, X2 >= 0, X2263 >= 0
   mark(z) -{ 2 }-> a__and(a__isNatKind(X444), X2) :|: z = 1 + (1 + X444) + X2, X444 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__isNat(X441), X2) :|: z = 1 + (1 + X441) + X2, X441 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__and(mark(X1264), X2264), X2) :|: X2264 >= 0, z = 1 + (1 + X1264 + X2264) + X2, X1264 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U41(mark(X1262), X2262, X3117), X2) :|: X1262 >= 0, X3117 >= 0, X2262 >= 0, X2 >= 0, z = 1 + (1 + X1262 + X2262 + X3117) + X2
   mark(z) -{ 2 }-> a__and(a__U31(mark(X1261), X2261), X2) :|: z = 1 + (1 + X1261 + X2261) + X2, X2261 >= 0, X2 >= 0, X1261 >= 0
   mark(z) -{ 2 }-> a__and(a__U22(mark(X443)), X2) :|: z = 1 + (1 + X443) + X2, X443 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U21(mark(X1260), X2260), X2) :|: z = 1 + (1 + X1260 + X2260) + X2, X2260 >= 0, X1260 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U13(mark(X442)), X2) :|: X442 >= 0, z = 1 + (1 + X442) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U12(mark(X1259), X2259), X2) :|: X2259 >= 0, X2 >= 0, z = 1 + (1 + X1259 + X2259) + X2, X1259 >= 0
   mark(z) -{ 2 }-> a__and(a__U11(mark(X1258), X2258, X3116), X2) :|: z = 1 + (1 + X1258 + X2258 + X3116) + X2, X2258 >= 0, X3116 >= 0, X2 >= 0, X1258 >= 0
   mark(z) -{ 2 }-> a__and(1, z - 2) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__and(0, z - 1) :|: z - 1 >= 0
   mark(z) -{ 2 }-> a__and(1 + mark(X445), X2) :|: z = 1 + (1 + X445) + X2, X2 >= 0, X445 >= 0
   mark(z) -{ 2 }-> a__U41(a__plus(mark(X1151), mark(X2151)), X2, X3) :|: X2151 >= 0, X3 >= 0, X1151 >= 0, z = 1 + (1 + X1151 + X2151) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__isNatKind(X350), X2, X3) :|: X350 >= 0, z = 1 + (1 + X350) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__isNat(X346), X2, X3) :|: X3 >= 0, z = 1 + (1 + X346) + X2 + X3, X346 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__and(mark(X1152), X2152), X2, X3) :|: z = 1 + (1 + X1152 + X2152) + X2 + X3, X2152 >= 0, X3 >= 0, X2 >= 0, X1152 >= 0
   mark(z) -{ 2 }-> a__U41(a__U41(mark(X1150), X2150, X349), X2, X3) :|: X2150 >= 0, z = 1 + (1 + X1150 + X2150 + X349) + X2 + X3, X3 >= 0, X349 >= 0, X1150 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U31(mark(X1149), X2149), X2, X3) :|: z = 1 + (1 + X1149 + X2149) + X2 + X3, X2149 >= 0, X3 >= 0, X2 >= 0, X1149 >= 0
   mark(z) -{ 2 }-> a__U41(a__U22(mark(X348)), X2, X3) :|: z = 1 + (1 + X348) + X2 + X3, X3 >= 0, X348 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U21(mark(X1148), X2148), X2, X3) :|: X2148 >= 0, z = 1 + (1 + X1148 + X2148) + X2 + X3, X3 >= 0, X1148 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U13(mark(X347)), X2, X3) :|: X347 >= 0, z = 1 + (1 + X347) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U12(mark(X1147), X2147), X2, X3) :|: X1147 >= 0, X3 >= 0, X2147 >= 0, X2 >= 0, z = 1 + (1 + X1147 + X2147) + X2 + X3
   mark(z) -{ 2 }-> a__U41(a__U11(mark(X1146), X2146, X345), X2, X3) :|: z = 1 + (1 + X1146 + X2146 + X345) + X2 + X3, X1146 >= 0, X345 >= 0, X3 >= 0, X2146 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(1 + mark(X351), X2, X3) :|: z = 1 + (1 + X351) + X2 + X3, X3 >= 0, X351 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__plus(mark(X1144), mark(X2144)), X2) :|: X2144 >= 0, z = 1 + (1 + X1144 + X2144) + X2, X1144 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__isNatKind(X308), X2) :|: z = 1 + (1 + X308) + X2, X308 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__isNat(X305), X2) :|: X305 >= 0, z = 1 + (1 + X305) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__and(mark(X1145), X2145), X2) :|: z = 1 + (1 + X1145 + X2145) + X2, X1145 >= 0, X2 >= 0, X2145 >= 0
   mark(z) -{ 2 }-> a__U31(a__U41(mark(X1143), X2143, X344), X2) :|: X344 >= 0, z = 1 + (1 + X1143 + X2143 + X344) + X2, X2143 >= 0, X2 >= 0, X1143 >= 0
   mark(z) -{ 2 }-> a__U31(a__U31(mark(X1142), X2142), X2) :|: z = 1 + (1 + X1142 + X2142) + X2, X2142 >= 0, X2 >= 0, X1142 >= 0
   mark(z) -{ 2 }-> a__U31(a__U22(mark(X307)), X2) :|: z = 1 + (1 + X307) + X2, X307 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U21(mark(X1141), X2141), X2) :|: X2141 >= 0, z = 1 + (1 + X1141 + X2141) + X2, X2 >= 0, X1141 >= 0
   mark(z) -{ 2 }-> a__U31(a__U13(mark(X306)), X2) :|: z = 1 + (1 + X306) + X2, X306 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U12(mark(X1140), X2140), X2) :|: X2140 >= 0, z = 1 + (1 + X1140 + X2140) + X2, X1140 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U11(mark(X1139), X2139, X343), X2) :|: X343 >= 0, X2139 >= 0, z = 1 + (1 + X1139 + X2139 + X343) + X2, X2 >= 0, X1139 >= 0
   mark(z) -{ 2 }-> a__U31(1, z - 2) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U31(0, z - 1) :|: z - 1 >= 0
   mark(z) -{ 2 }-> a__U31(1 + mark(X309), X2) :|: X309 >= 0, z = 1 + (1 + X309) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U22(a__plus(mark(X1137), mark(X2137))) :|: X2137 >= 0, X1137 >= 0, z = 1 + (1 + X1137 + X2137)
   mark(z) -{ 2 }-> a__U22(a__isNatKind(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U22(a__isNat(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U22(a__and(mark(X1138), X2138)) :|: X2138 >= 0, z = 1 + (1 + X1138 + X2138), X1138 >= 0
   mark(z) -{ 2 }-> a__U22(a__U41(mark(X1136), X2136, X342)) :|: z = 1 + (1 + X1136 + X2136 + X342), X342 >= 0, X1136 >= 0, X2136 >= 0
   mark(z) -{ 2 }-> a__U22(a__U31(mark(X1135), X2135)) :|: X1135 >= 0, z = 1 + (1 + X1135 + X2135), X2135 >= 0
   mark(z) -{ 2 }-> a__U22(a__U22(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U22(a__U21(mark(X1134), X2134)) :|: X2134 >= 0, z = 1 + (1 + X1134 + X2134), X1134 >= 0
   mark(z) -{ 2 }-> a__U22(a__U13(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U22(a__U12(mark(X1133), X2133)) :|: z = 1 + (1 + X1133 + X2133), X2133 >= 0, X1133 >= 0
   mark(z) -{ 2 }-> a__U22(a__U11(mark(X1132), X2132, X341)) :|: z = 1 + (1 + X1132 + X2132 + X341), X341 >= 0, X2132 >= 0, X1132 >= 0
   mark(z) -{ 2 }-> a__U22(1 + mark(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U21(a__plus(mark(X1130), mark(X2130)), X2) :|: X2130 >= 0, X1130 >= 0, z = 1 + (1 + X1130 + X2130) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__isNatKind(X208), X2) :|: z = 1 + (1 + X208) + X2, X208 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__isNat(X205), X2) :|: X205 >= 0, z = 1 + (1 + X205) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__and(mark(X1131), X2131), X2) :|: z = 1 + (1 + X1131 + X2131) + X2, X2131 >= 0, X2 >= 0, X1131 >= 0
   mark(z) -{ 2 }-> a__U21(a__U41(mark(X1129), X2129, X340), X2) :|: X1129 >= 0, z = 1 + (1 + X1129 + X2129 + X340) + X2, X2129 >= 0, X340 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U31(mark(X1128), X2128), X2) :|: z = 1 + (1 + X1128 + X2128) + X2, X2128 >= 0, X1128 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U22(mark(X207)), X2) :|: z = 1 + (1 + X207) + X2, X207 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U21(mark(X1127), X2127), X2) :|: z = 1 + (1 + X1127 + X2127) + X2, X2127 >= 0, X1127 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U13(mark(X206)), X2) :|: X206 >= 0, z = 1 + (1 + X206) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U12(mark(X1126), X2126), X2) :|: z = 1 + (1 + X1126 + X2126) + X2, X1126 >= 0, X2 >= 0, X2126 >= 0
   mark(z) -{ 2 }-> a__U21(a__U11(mark(X1125), X2125, X339), X2) :|: X1125 >= 0, X339 >= 0, z = 1 + (1 + X1125 + X2125 + X339) + X2, X2 >= 0, X2125 >= 0
   mark(z) -{ 2 }-> a__U21(1, z - 2) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U21(0, z - 1) :|: z - 1 >= 0
   mark(z) -{ 2 }-> a__U21(1 + mark(X209), X2) :|: z = 1 + (1 + X209) + X2, X209 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U13(a__plus(mark(X1123), mark(X2123))) :|: X2123 >= 0, X1123 >= 0, z = 1 + (1 + X1123 + X2123)
   mark(z) -{ 2 }-> a__U13(a__isNatKind(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U13(a__isNat(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U13(a__and(mark(X1124), X2124)) :|: X1124 >= 0, z = 1 + (1 + X1124 + X2124), X2124 >= 0
   mark(z) -{ 2 }-> a__U13(a__U41(mark(X1122), X2122, X338)) :|: X2122 >= 0, X338 >= 0, z = 1 + (1 + X1122 + X2122 + X338), X1122 >= 0
   mark(z) -{ 2 }-> a__U13(a__U31(mark(X1121), X2121)) :|: X1121 >= 0, z = 1 + (1 + X1121 + X2121), X2121 >= 0
   mark(z) -{ 2 }-> a__U13(a__U22(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U13(a__U21(mark(X1120), X2120)) :|: z = 1 + (1 + X1120 + X2120), X2120 >= 0, X1120 >= 0
   mark(z) -{ 2 }-> a__U13(a__U13(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U13(a__U12(mark(X1119), X2119)) :|: z = 1 + (1 + X1119 + X2119), X1119 >= 0, X2119 >= 0
   mark(z) -{ 2 }-> a__U13(a__U11(mark(X1118), X2118, X337)) :|: z = 1 + (1 + X1118 + X2118 + X337), X1118 >= 0, X2118 >= 0, X337 >= 0
   mark(z) -{ 2 }-> a__U13(1 + mark(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U12(a__plus(mark(X1116), mark(X2116)), X2) :|: z = 1 + (1 + X1116 + X2116) + X2, X1116 >= 0, X2 >= 0, X2116 >= 0
   mark(z) -{ 2 }-> a__U12(a__isNatKind(X108), X2) :|: z = 1 + (1 + X108) + X2, X2 >= 0, X108 >= 0
   mark(z) -{ 2 }-> a__U12(a__isNat(X105), X2) :|: X105 >= 0, z = 1 + (1 + X105) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__and(mark(X1117), X2117), X2) :|: X2117 >= 0, z = 1 + (1 + X1117 + X2117) + X2, X1117 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U41(mark(X1115), X2115, X336), X2) :|: z = 1 + (1 + X1115 + X2115 + X336) + X2, X1115 >= 0, X2 >= 0, X336 >= 0, X2115 >= 0
   mark(z) -{ 2 }-> a__U12(a__U31(mark(X1114), X2114), X2) :|: X1114 >= 0, z = 1 + (1 + X1114 + X2114) + X2, X2 >= 0, X2114 >= 0
   mark(z) -{ 2 }-> a__U12(a__U22(mark(X107)), X2) :|: X107 >= 0, z = 1 + (1 + X107) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U21(mark(X1113), X2113), X2) :|: z = 1 + (1 + X1113 + X2113) + X2, X2113 >= 0, X1113 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U13(mark(X106)), X2) :|: X106 >= 0, z = 1 + (1 + X106) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U12(mark(X1112), X2112), X2) :|: z = 1 + (1 + X1112 + X2112) + X2, X2112 >= 0, X2 >= 0, X1112 >= 0
   mark(z) -{ 2 }-> a__U12(a__U11(mark(X1111), X2111, X335), X2) :|: X1111 >= 0, z = 1 + (1 + X1111 + X2111 + X335) + X2, X2111 >= 0, X335 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(1, z - 2) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U12(0, z - 1) :|: z - 1 >= 0
   mark(z) -{ 2 }-> a__U12(1 + mark(X109), X2) :|: X2 >= 0, z = 1 + (1 + X109) + X2, X109 >= 0
   mark(z) -{ 2 }-> a__U11(a__plus(mark(X1109), mark(X2109)), X2, X3) :|: z = 1 + (1 + X1109 + X2109) + X2 + X3, X2109 >= 0, X3 >= 0, X2 >= 0, X1109 >= 0
   mark(z) -{ 2 }-> a__U11(a__isNatKind(X103), X2, X3) :|: X103 >= 0, z = 1 + (1 + X103) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__isNat(X100), X2, X3) :|: z = 1 + (1 + X100) + X2 + X3, X3 >= 0, X2 >= 0, X100 >= 0
   mark(z) -{ 2 }-> a__U11(a__and(mark(X1110), X2110), X2, X3) :|: X1110 >= 0, X2110 >= 0, z = 1 + (1 + X1110 + X2110) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U41(mark(X1108), X2108, X334), X2, X3) :|: X1108 >= 0, z = 1 + (1 + X1108 + X2108 + X334) + X2 + X3, X3 >= 0, X2108 >= 0, X334 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U31(mark(X1107), X2107), X2, X3) :|: X2107 >= 0, X1107 >= 0, z = 1 + (1 + X1107 + X2107) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U22(mark(X102)), X2, X3) :|: z = 1 + (1 + X102) + X2 + X3, X3 >= 0, X2 >= 0, X102 >= 0
   mark(z) -{ 2 }-> a__U11(a__U21(mark(X1106), X2106), X2, X3) :|: X2106 >= 0, z = 1 + (1 + X1106 + X2106) + X2 + X3, X1106 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U13(mark(X101)), X2, X3) :|: X3 >= 0, X2 >= 0, z = 1 + (1 + X101) + X2 + X3, X101 >= 0
   mark(z) -{ 2 }-> a__U11(a__U12(mark(X1105), X2105), X2, X3) :|: z = 1 + (1 + X1105 + X2105) + X2 + X3, X1105 >= 0, X3 >= 0, X2 >= 0, X2105 >= 0
   mark(z) -{ 2 }-> a__U11(a__U11(mark(X1104), X2104, X333), X2, X3) :|: X1104 >= 0, X333 >= 0, z = 1 + (1 + X1104 + X2104 + X333) + X2 + X3, X3 >= 0, X2104 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(1 + mark(X104), X2, X3) :|: X104 >= 0, X3 >= 0, z = 1 + (1 + X104) + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 3 }-> 1 :|: z = 1 + 1, 1 = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0


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(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

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(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__U11(tt, V1, V2) -> a__U12(a__isNat(V1), V2) [1]
   a__U12(tt, V2) -> a__U13(a__isNat(V2)) [1]
   a__U13(tt) -> tt [1]
   a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1]
   a__U22(tt) -> tt [1]
   a__U31(tt, N) -> mark(N) [1]
   a__U41(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(V1, V2)) -> a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2) [1]
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1]
   a__isNatKind(0) -> tt [1]
   a__isNatKind(plus(V1, V2)) -> a__and(a__isNatKind(V1), isNatKind(V2)) [1]
   a__isNatKind(s(V1)) -> a__isNatKind(V1) [1]
   a__plus(N, 0) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N) [1]
   a__plus(N, s(M)) -> a__U41(a__and(a__and(a__isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N) [1]
   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1]
   mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U13(X)) -> a__U13(mark(X)) [1]
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1]
   mark(U22(X)) -> a__U22(mark(X)) [1]
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), X2) [1]
   mark(isNatKind(X)) -> a__isNatKind(X) [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(0) -> 0 [1]
   a__U11(X1, X2, X3) -> U11(X1, X2, X3) [1]
   a__U12(X1, X2) -> U12(X1, X2) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U13(X) -> U13(X) [1]
   a__U21(X1, X2) -> U21(X1, X2) [1]
   a__U22(X) -> U22(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNatKind(X) -> isNatKind(X) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
tt :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
mark :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
s :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
0 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
plus :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
a__isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
isNatKind :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
and :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
isNat :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U11 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U12 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U13 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U21 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U22 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U31 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41
U41 :: tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41 -> tt:s:0:plus:isNatKind:isNat:and:U11:U12:U13:U21:U22:U31:U41

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:

   tt => 1
   0 => 0

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

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

   a__U11(z, z', z'') -{ 1 }-> a__U12(a__isNat(V1), V2) :|: V1 >= 0, z = 1, V2 >= 0, z'' = V2, z' = V1
   a__U11(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U12(z, z') -{ 1 }-> a__U13(a__isNat(V2)) :|: z' = V2, z = 1, V2 >= 0
   a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U13(z) -{ 1 }-> 1 :|: z = 1
   a__U13(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U21(z, z') -{ 1 }-> a__U22(a__isNat(V1)) :|: V1 >= 0, z = 1, z' = V1
   a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U22(z) -{ 1 }-> 1 :|: z = 1
   a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U31(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0
   a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U41(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__and(z, z') -{ 1 }-> mark(X) :|: z' = X, z = 1, 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__and(a__isNatKind(V1), 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNat(z) -{ 1 }-> 1 :|: z = 0
   a__isNat(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__and(a__isNatKind(V1), 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatKind(z) -{ 1 }-> 1 :|: z = 0
   a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__plus(z, z') -{ 1 }-> a__U41(a__and(a__and(a__isNat(M), 1 + M), 1 + (1 + N) + (1 + N)), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__plus(z, z') -{ 1 }-> a__U31(a__and(a__isNat(N), 1 + N), N) :|: z = N, z' = 0, N >= 0
   a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__isNatKind(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__U41(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 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__U13(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U12(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U11(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0

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__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0))
   A__U11(z0, z1, z2) -> c1
   A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0))
   A__U12(z0, z1) -> c3
   A__U13(tt) -> c4
   A__U13(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(MARK(z0))
   A__U31(z0, z1) -> c11
   A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U41(z0, z1, z2) -> c14
   A__AND(tt, z0) -> c15(MARK(z0))
   A__AND(z0, z1) -> c16
   A__ISNAT(0) -> c17
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNAT(z0) -> c20
   A__ISNATKIND(0) -> c21
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__ISNATKIND(z0) -> c24
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   A__PLUS(z0, z1) -> c27
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(tt) -> c40
   MARK(s(z0)) -> c41(MARK(z0))
   MARK(0) -> c42
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0))
   A__U11(z0, z1, z2) -> c1
   A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0))
   A__U12(z0, z1) -> c3
   A__U13(tt) -> c4
   A__U13(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(MARK(z0))
   A__U31(z0, z1) -> c11
   A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U41(z0, z1, z2) -> c14
   A__AND(tt, z0) -> c15(MARK(z0))
   A__AND(z0, z1) -> c16
   A__ISNAT(0) -> c17
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNAT(z0) -> c20
   A__ISNATKIND(0) -> c21
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__ISNATKIND(z0) -> c24
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   A__PLUS(z0, z1) -> c27
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(tt) -> c40
   MARK(s(z0)) -> c41(MARK(z0))
   MARK(0) -> c42
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U12_2, A__U13_1, A__U21_2, A__U22_1, A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1

Compound Symbols:   c_2, c1, c2_2, c3, c4, c5, c6_2, c7, c8, c9, c10_1, c11, c12_2, c13_2, c14, c15_1, c16, c17, c18_3, c19_2, c20, c21, c22_2, c23_1, c24, c25_3, c26_4, c27, c28_2, c29_2, c30_1, c31_2, c32_2, c33_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c40, c41_1, c42


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

(25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 17 trailing nodes:
   A__PLUS(z0, z1) -> c27
   A__U22(tt) -> c8
   A__U12(z0, z1) -> c3
   A__ISNATKIND(z0) -> c24
   A__AND(z0, z1) -> c16
   A__U31(z0, z1) -> c11
   MARK(tt) -> c40
   A__ISNATKIND(0) -> c21
   A__U13(tt) -> c4
   A__ISNAT(0) -> c17
   A__U13(z0) -> c5
   A__ISNAT(z0) -> c20
   A__U21(z0, z1) -> c7
   A__U11(z0, z1, z2) -> c1
   MARK(0) -> c42
   A__U41(z0, z1, z2) -> c14
   A__U22(z0) -> c9

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

(26)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0))
   A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0))
   A__U31(tt, z0) -> c10(MARK(z0))
   A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0))
   A__U12(tt, z0) -> c2(A__U13(a__isNat(z0)), A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0))
   A__U31(tt, z0) -> c10(MARK(z0))
   A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(A__U13(mark(z0)), MARK(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U22(z0)) -> c33(A__U22(mark(z0)), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U12_2, A__U21_2, A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1

Compound Symbols:   c_2, c2_2, c6_2, c10_1, c12_2, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c31_2, c32_2, c33_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1


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

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

(28)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0))
   A__U31(tt, z0) -> c10(MARK(z0))
   A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0))
   A__U31(tt, z0) -> c10(MARK(z0))
   A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2

Compound Symbols:   c_2, c10_1, c12_2, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1


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

(29) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U11(tt, z0, z1) -> c(A__U12(a__isNat(z0), z1), A__ISNAT(z0)) by 
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1), A__ISNAT(0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, z0, x1) -> c(A__U12(isNat(z0), x1), A__ISNAT(z0))

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

(30)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1), A__ISNAT(0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, z0, x1) -> c(A__U12(isNat(z0), x1), A__ISNAT(z0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1), A__ISNAT(0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, z0, x1) -> c(A__U12(isNat(z0), x1), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3

Compound Symbols:   c10_1, c12_2, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2


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

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

(32)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3

Compound Symbols:   c10_1, c12_2, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1


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

(33) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, z0, z1) -> c12(A__PLUS(mark(z1), mark(z0)), MARK(z1)) by 
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, tt, x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)), MARK(0))

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

(34)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, tt, x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, tt, x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3

Compound Symbols:   c10_1, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2


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

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__U41_3, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3

Compound Symbols:   c10_1, c13_2, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1


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

(37) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, z0, z1) -> c13(A__PLUS(mark(z1), mark(z0)), MARK(z0)) by 
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, tt, x1) -> c13(A__PLUS(mark(x1), tt), MARK(tt))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, tt, x1) -> c13(A__PLUS(mark(x1), tt), MARK(tt))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, tt, x1) -> c13(A__PLUS(mark(x1), tt), MARK(tt))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3

Compound Symbols:   c10_1, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2


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

(39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U41(tt, tt, x1) -> c13(A__PLUS(mark(x1), tt), MARK(tt))

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0), MARK(0))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3

Compound Symbols:   c10_1, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2


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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3

Compound Symbols:   c10_1, c15_1, c18_3, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1


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

(43) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNAT(plus(z0, z1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) by 
   A__ISNAT(plus(x0, x1)) -> c18(A__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)), A__ISNATKIND(0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(x0, x1)) -> c18(A__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)), A__ISNATKIND(0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(x0, x1)) -> c18(A__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)), A__ISNATKIND(0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3

Compound Symbols:   c10_1, c15_1, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3


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

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNAT_1, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3

Compound Symbols:   c10_1, c15_1, c19_2, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2


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

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNAT(s(z0)) -> c19(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) by 
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0), A__ISNATKIND(0))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(z0)) -> c19(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0), A__ISNATKIND(0))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(z0)) -> c19(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0), A__ISNATKIND(0))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(z0)) -> c19(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1

Compound Symbols:   c10_1, c15_1, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2


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

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1

Compound Symbols:   c10_1, c15_1, c22_2, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATKIND(plus(z0, z1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(z1)), A__ISNATKIND(z0)) by 
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)), A__ISNATKIND(0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__AND(isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)), A__ISNATKIND(0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__AND(isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)), A__ISNATKIND(0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__AND(isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1

Compound Symbols:   c10_1, c15_1, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2


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

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1

Compound Symbols:   c10_1, c15_1, c23_1, c25_3, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__PLUS(z0, 0) -> c25(A__U31(a__and(a__isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0)) by 
   A__PLUS(x0, 0) -> c25(A__U31(and(a__isNat(x0), isNatKind(x0)), x0), A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(x0, 0) -> c25(A__U31(and(a__isNat(x0), isNatKind(x0)), x0), A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(x0, 0) -> c25(A__U31(and(a__isNat(x0), isNatKind(x0)), x0), A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1

Compound Symbols:   c10_1, c15_1, c23_1, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3


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

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, A__PLUS_2, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1

Compound Symbols:   c10_1, c15_1, c23_1, c26_4, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__PLUS(z0, s(z1)) -> c26(A__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0), A__AND(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNat(z1), isNatKind(z1)), A__ISNAT(z1)) by 
   A__PLUS(x0, s(x1)) -> c26(A__U41(and(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(and(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(and(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)), A__ISNAT(0))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4


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

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c28_2, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U11(z0, z1, z2)) -> c28(A__U11(mark(z0), z1, z2), MARK(z0)) by 
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt))
   MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U11(0, x1, x2)) -> c28(A__U11(0, x1, x2), MARK(0))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt))
   MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U11(0, x1, x2)) -> c28(A__U11(0, x1, x2), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt))
   MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U11(0, x1, x2)) -> c28(A__U11(0, x1, x2), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2


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

(65) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U11(0, x1, x2)) -> c28(A__U11(0, x1, x2), MARK(0))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt))
   MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2), MARK(tt))
   MARK(U11(s(z0), x1, x2)) -> c28(A__U11(s(mark(z0)), x1, x2), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2


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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c29_2, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1


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

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U12(z0, z1)) -> c29(A__U12(mark(z0), z1), MARK(z0)) by 
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt))
   MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U12(0, x1)) -> c29(A__U12(0, x1), MARK(0))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt))
   MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U12(0, x1)) -> c29(A__U12(0, x1), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt))
   MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U12(0, x1)) -> c29(A__U12(0, x1), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2


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

(71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U12(0, x1)) -> c29(A__U12(0, x1), MARK(0))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt))
   MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1), MARK(tt))
   MARK(U12(s(z0), x1)) -> c29(A__U12(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2


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

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c32_2, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U21(z0, z1)) -> c32(A__U21(mark(z0), z1), MARK(z0)) by 
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt))
   MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U21(0, x1)) -> c32(A__U21(0, x1), MARK(0))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt))
   MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U21(0, x1)) -> c32(A__U21(0, x1), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt))
   MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U21(0, x1)) -> c32(A__U21(0, x1), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2


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

(77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U21(0, x1)) -> c32(A__U21(0, x1), MARK(0))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt))
   MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1), MARK(tt))
   MARK(U21(s(z0), x1)) -> c32(A__U21(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2


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

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c34_2, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1


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

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U31(z0, z1)) -> c34(A__U31(mark(z0), z1), MARK(z0)) by 
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U31(0, x1)) -> c34(A__U31(0, x1), MARK(0))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U31(0, x1)) -> c34(A__U31(0, x1), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U31(0, x1)) -> c34(A__U31(0, x1), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2


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

(83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U31(0, x1)) -> c34(A__U31(0, x1), MARK(0))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c34(A__U31(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2


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

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c35_2, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U41(z0, z1, z2)) -> c35(A__U41(mark(z0), z1, z2), MARK(z0)) by 
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U41(0, x1, x2)) -> c35(A__U41(0, x1, x2), MARK(0))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U41(0, x1, x2)) -> c35(A__U41(0, x1, x2), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U41(0, x1, x2)) -> c35(A__U41(0, x1, x2), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2


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

(89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U41(0, x1, x2)) -> c35(A__U41(0, x1, x2), MARK(0))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
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   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
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   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
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   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
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   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
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   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
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   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
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   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
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   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
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   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c35(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2


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

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c36_2, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1


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

(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(plus(z0, z1)) -> c36(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by 
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, tt)) -> c36(A__PLUS(mark(x0), tt), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)), MARK(tt))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)), MARK(0))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
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   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
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   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)), MARK(tt))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, tt)) -> c36(A__PLUS(mark(x0), tt), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)), MARK(tt))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2


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

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c37_2, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1


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

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(plus(z0, z1)) -> c37(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by 
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, tt)) -> c37(A__PLUS(mark(x0), tt), MARK(tt))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, tt)) -> c37(A__PLUS(mark(x0), tt), MARK(tt))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
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   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
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   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
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   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
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   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
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   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
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   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, tt)) -> c37(A__PLUS(mark(x0), tt), MARK(tt))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2


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

(99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(plus(x0, tt)) -> c37(A__PLUS(mark(x0), tt), MARK(tt))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
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   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2


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

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
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   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
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   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
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   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c38_2, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1


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

(103) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(and(z0, z1)) -> c38(A__AND(mark(z0), z1), MARK(z0)) by 
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt))
   MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0)))
   MARK(and(0, x1)) -> c38(A__AND(0, x1), MARK(0))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt))
   MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0)))
   MARK(and(0, x1)) -> c38(A__AND(0, x1), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
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   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
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   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
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   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
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   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
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   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
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   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
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   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
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   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
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   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
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   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
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   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt))
   MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0)))
   MARK(and(0, x1)) -> c38(A__AND(0, x1), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2


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

(105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(and(0, x1)) -> c38(A__AND(0, x1), MARK(0))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
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   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt))
   MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1), MARK(tt))
   MARK(and(s(z0), x1)) -> c38(A__AND(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2


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

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
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   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
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   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
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   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
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   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
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   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c38(MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1)))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c38(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1


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

(109) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U11(tt, plus(z0, z1), x1) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), x1), A__ISNAT(plus(z0, z1))) by 
   A__U11(tt, plus(z1, z2), x2) -> c(A__U12(U11(a__and(a__isNatKind(z1), isNatKind(z2)), z1, z2), x2), A__ISNAT(plus(z1, z2)))
   A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1)))
   A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1)))
   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c38(MARK(s(z0)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__U12(U11(a__and(a__isNatKind(z1), isNatKind(z2)), z1, z2), x2), A__ISNAT(plus(z1, z2)))
   A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1)))
   A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1)))
   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
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   MARK(and(tt, x1)) -> c38(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c38(MARK(s(z0)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__U12(U11(a__and(a__isNatKind(z1), isNatKind(z2)), z1, z2), x2), A__ISNAT(plus(z1, z2)))
   A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1)))
   A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1)))
   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1


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

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c38(MARK(s(z0)))
   A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1)))
   A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1)))
   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
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   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c38(MARK(s(z0)))
   A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1)))
   A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1)))
   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_2, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1


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

(113) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) by 
   A__U11(tt, s(z1), x1) -> c(A__U12(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1)))
   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
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   A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1)))
   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
   A__U11(tt, s(z1), x1) -> c(A__U12(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1)))
   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c38(MARK(s(z0)))
   A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1)))
   A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1)))
   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
   A__U11(tt, s(z1), x1) -> c(A__U12(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1)))
   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
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   A__U41(tt, tt, x1) -> c12(MARK(x1))
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   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
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   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
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   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
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   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
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   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
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   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
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   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
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   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
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   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
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   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
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   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
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   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
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   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c38(MARK(s(z0)))
   A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1)))
   A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1)))
   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c38(MARK(s(z0)))
   A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1)))
   A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1)))
   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, U11(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) by 
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(x3))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
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   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
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   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c38(MARK(s(z0)))
   A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1)))
   A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1)))
   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
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   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
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   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
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   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
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   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
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   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
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   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
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   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
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   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
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   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNatKind(z0))) -> c36(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c36(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c36(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c36(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1), x1)) -> c36(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c36(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U13(z0), x1)) -> c36(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(U13(z0)))
   MARK(plus(U21(z0, z1), x1)) -> c36(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(plus(U22(z0), x1)) -> c36(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c36(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c36(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c36(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c36(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNatKind(z0), x1)) -> c36(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(plus(s(z0), x1)) -> c36(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c36(MARK(x0))
   MARK(plus(tt, x1)) -> c36(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c36(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1))) -> c37(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c37(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U13(z0))) -> c37(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(U13(z0)))
   MARK(plus(x0, U21(z0, z1))) -> c37(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(plus(x0, U22(z0))) -> c37(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c37(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c37(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c37(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c37(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNatKind(z0))) -> c37(A__PLUS(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(plus(x0, s(z0))) -> c37(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c37(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1), x1)) -> c37(A__PLUS(a__U12(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c37(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U13(z0), x1)) -> c37(A__PLUS(a__U13(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1), x1)) -> c37(A__PLUS(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U22(z0), x1)) -> c37(A__PLUS(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c37(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c37(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c37(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c37(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNatKind(z0), x1)) -> c37(A__PLUS(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c37(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c37(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c37(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c37(A__PLUS(mark(x0), 0))
   MARK(and(U11(z0, z1, z2), x1)) -> c38(A__AND(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(and(U12(z0, z1), x1)) -> c38(A__AND(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c38(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U13(z0), x1)) -> c38(A__AND(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(and(U21(z0, z1), x1)) -> c38(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c38(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(U31(z0, z1), x1)) -> c38(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U41(z0, z1, z2), x1)) -> c38(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c38(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c38(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatKind(z0), x1)) -> c38(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(tt, x1)) -> c38(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c38(MARK(s(z0)))
   A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1)))
   A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1)))
   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(121) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, U12(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(x1)) by 
   A__U41(tt, U12(x0, z1), x2) -> c12(A__PLUS(mark(x2), U12(mark(x0), z1)), MARK(x2))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)), MARK(tt))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)), MARK(0))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
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   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(x0, z1), x2) -> c12(A__PLUS(mark(x2), U12(mark(x0), z1)), MARK(x2))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)), MARK(tt))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
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   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(x0, z1), x2) -> c12(A__PLUS(mark(x2), U12(mark(x0), z1)), MARK(x2))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)), MARK(tt))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
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   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
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   A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1)))
   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(125) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) by 
   A__U41(tt, isNat(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), isNat(z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)), MARK(tt))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)), MARK(0))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
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   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
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   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
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   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)), MARK(tt))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
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   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(A__PLUS(mark(x1), isNat(z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)), MARK(tt))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
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   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
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   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(129) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, U13(z0), x1) -> c12(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(x1)) by 
   A__U41(tt, U13(x0), x1) -> c12(A__PLUS(mark(x1), U13(mark(x0))), MARK(x1))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))), MARK(tt))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))), MARK(0))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
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   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(x0), x1) -> c12(A__PLUS(mark(x1), U13(mark(x0))), MARK(x1))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))), MARK(tt))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
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   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(x0), x1) -> c12(A__PLUS(mark(x1), U13(mark(x0))), MARK(x1))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))), MARK(tt))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
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   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
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   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
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   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
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   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
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   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
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   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
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   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
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   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
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   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
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   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
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   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
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   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
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   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
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   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(133) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, U21(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(x1)) by 
   A__U41(tt, U21(x0, z1), x2) -> c12(A__PLUS(mark(x2), U21(mark(x0), z1)), MARK(x2))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)), MARK(tt))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)), MARK(0))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
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   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(x0, z1), x2) -> c12(A__PLUS(mark(x2), U21(mark(x0), z1)), MARK(x2))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)), MARK(tt))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)), MARK(tt))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
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   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
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   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
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   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
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   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
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   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
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   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(137) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, U22(z0), x1) -> c12(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(x1)) by 
   A__U41(tt, U22(x0), x1) -> c12(A__PLUS(mark(x1), U22(mark(x0))), MARK(x1))
   A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1))
   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))), MARK(tt))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))), MARK(0))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
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   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
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   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
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   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
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   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
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   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
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   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
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   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
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   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
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   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
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   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
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   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
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   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
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   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
   A__U41(tt, U22(x0), x1) -> c12(A__PLUS(mark(x1), U22(mark(x0))), MARK(x1))
   A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1))
   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))), MARK(tt))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
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   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
   A__U41(tt, U22(x0), x1) -> c12(A__PLUS(mark(x1), U22(mark(x0))), MARK(x1))
   A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1))
   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))), MARK(tt))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
   A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1))
   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
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   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
   A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1))
   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(141) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, U31(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) by 
   A__U41(tt, U31(x0, z1), x2) -> c12(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2))
   A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
   A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1))
   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
   A__U41(tt, U31(x0, z1), x2) -> c12(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2))
   A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
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   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
   A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1))
   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
   A__U41(tt, U31(x0, z1), x2) -> c12(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2))
   A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
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   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
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   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
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   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
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   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
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   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
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   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
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   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
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   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
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   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
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   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
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   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
   A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1))
   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
   A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
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   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
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   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
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   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
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   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
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   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
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   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
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   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
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   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
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   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
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   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c36(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
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   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
   A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1))
   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
   A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(145) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, U41(z0, z1, z2), x1) -> c12(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) by 
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
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   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
   A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
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   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
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   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
   A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1))
   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
   A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
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   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
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   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
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   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
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   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
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   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
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   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
   A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(149) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, plus(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) by 
   A__U41(tt, plus(x0, x1), x2) -> c12(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
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   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, x1), x2) -> c12(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
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   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
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   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
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   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
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   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
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   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
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   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
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   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(153) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, and(z0, z1), x1) -> c12(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) by 
   A__U41(tt, and(x0, z1), x2) -> c12(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)), MARK(0))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
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   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
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   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
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   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(x0, z1), x2) -> c12(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
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   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
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   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
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   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
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   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
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   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
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   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
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   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
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   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
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   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
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   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
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   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
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   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
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   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
   A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
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   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
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   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
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   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(x0, z1), x2) -> c12(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
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   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
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   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
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   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
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   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
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   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
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   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
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   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
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   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
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   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
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   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
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   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
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   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
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   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
   A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
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   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
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   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
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   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(157) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1)) by 
   A__U41(tt, isNatKind(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)), MARK(tt))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)), MARK(0))

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
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   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
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   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
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   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
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   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
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   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)), MARK(tt))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
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   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
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   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(0), x1) -> c12(A__PLUS(mark(x1), tt), MARK(x1))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(A__PLUS(mark(x1), isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)), MARK(tt))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
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   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
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   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
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   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
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   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
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   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
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   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
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   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
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   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c36(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c36(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
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   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
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   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
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   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
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   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
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   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
   A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
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   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
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   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
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   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
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   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
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   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
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   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
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   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
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   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(161) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, x0, U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) by 
   A__U41(tt, U11(z0, z1, z2), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U11(x1, x2, x3)))
   A__U41(tt, U12(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U12(mark(z0), z1)), MARK(U11(x1, x2, x3)))
   A__U41(tt, isNat(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__isNat(z0)), MARK(U11(x1, x2, x3)))
   A__U41(tt, U13(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U13(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, U21(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U21(mark(z0), z1)), MARK(U11(x1, x2, x3)))
   A__U41(tt, U22(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U22(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, U31(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U31(mark(z0), z1)), MARK(U11(x1, x2, x3)))
   A__U41(tt, U41(z0, z1, z2), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__U41(mark(z0), z1, z2)), MARK(U11(x1, x2, x3)))
   A__U41(tt, plus(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U11(x1, x2, x3)))
   A__U41(tt, and(z0, z1), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__and(mark(z0), z1)), MARK(U11(x1, x2, x3)))
   A__U41(tt, isNatKind(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), a__isNatKind(z0)), MARK(U11(x1, x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3)))
   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(U11(0, x2, x3)))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3)))
   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(U11(0, x2, x3)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
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   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
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   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
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   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
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   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
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   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
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   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
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   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
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   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
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   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
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   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
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   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
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   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
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   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
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   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3)))
   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(U11(0, x2, x3)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
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   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)))
   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
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   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)))
   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(165) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, x0, U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(U12(z0, z1))) by 
   A__U41(tt, U11(z0, z1, z2), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U11(mark(z0), z1, z2)), MARK(U12(x1, x2)))
   A__U41(tt, U12(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U12(mark(z0), z1)), MARK(U12(x1, x2)))
   A__U41(tt, isNat(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__isNat(z0)), MARK(U12(x1, x2)))
   A__U41(tt, U13(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U13(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, U21(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U21(mark(z0), z1)), MARK(U12(x1, x2)))
   A__U41(tt, U22(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U22(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, U31(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U12(x1, x2)))
   A__U41(tt, U41(z0, z1, z2), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U12(x1, x2)))
   A__U41(tt, plus(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U12(x1, x2)))
   A__U41(tt, and(z0, z1), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__and(mark(z0), z1)), MARK(U12(x1, x2)))
   A__U41(tt, isNatKind(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), a__isNatKind(z0)), MARK(U12(x1, x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), tt), MARK(U12(x1, x2)))
   A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1)))
   A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2)))
   A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2)))
   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)), MARK(U12(0, x2)))

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
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   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
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   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
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   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
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   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
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   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
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   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
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   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
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   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
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   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
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   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
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   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
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   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
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   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
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   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)))
   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), tt), MARK(U12(x1, x2)))
   A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1)))
   A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2)))
   A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2)))
   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)), MARK(U12(0, x2)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
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   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
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   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
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   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
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   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
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   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
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   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
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   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
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   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
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   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)))
   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), tt), MARK(U12(x1, x2)))
   A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1)))
   A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2)))
   A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2)))
   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)), MARK(U12(0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
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   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
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   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
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   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
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   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
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   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
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   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
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   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
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   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
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   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
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   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1)))
   A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2)))
   A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2)))
   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
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   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
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   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
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   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
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   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
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   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1))
   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
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   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
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   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
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   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
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   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
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   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
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   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
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   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)))
   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1)))
   A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2)))
   A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2)))
   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(169) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) by 
   A__U41(tt, U11(z0, z1, z2), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U11(mark(z0), z1, z2)), MARK(isNat(x1)))
   A__U41(tt, U12(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U12(mark(z0), z1)), MARK(isNat(x1)))
   A__U41(tt, isNat(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__isNat(z0)), MARK(isNat(x1)))
   A__U41(tt, U13(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U13(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, U21(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U21(mark(z0), z1)), MARK(isNat(x1)))
   A__U41(tt, U22(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U22(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, U31(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U31(mark(z0), z1)), MARK(isNat(x1)))
   A__U41(tt, U41(z0, z1, z2), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__U41(mark(z0), z1, z2)), MARK(isNat(x1)))
   A__U41(tt, plus(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__plus(mark(z0), mark(z1))), MARK(isNat(x1)))
   A__U41(tt, and(z0, z1), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__and(mark(z0), z1)), MARK(isNat(x1)))
   A__U41(tt, isNatKind(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), a__isNatKind(z0)), MARK(isNat(x1)))
   A__U41(tt, tt, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1)))
   A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0))))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
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   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
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   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
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   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
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   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
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   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
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   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
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   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
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   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
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   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)))
   A__U41(tt, tt, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1)))
   A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0))))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
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   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)))
   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1)))
   A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2)))
   A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2)))
   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)))
   A__U41(tt, tt, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1)))
   A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0))))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
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   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
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   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
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   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
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   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
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   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
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   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
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   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
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   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
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   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)))
   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1)))
   A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2)))
   A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2)))
   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)))
   A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0))))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0)))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
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   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
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   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
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   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
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   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
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   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
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   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
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   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
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   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
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   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
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   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
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   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
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   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
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   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1)))
   A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2)))
   A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2)))
   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)))
   A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0))))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(173) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, x0, U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(U13(z0))) by 
   A__U41(tt, U11(z0, z1, z2), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U11(mark(z0), z1, z2)), MARK(U13(x1)))
   A__U41(tt, U12(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U12(mark(z0), z1)), MARK(U13(x1)))
   A__U41(tt, isNat(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__isNat(z0)), MARK(U13(x1)))
   A__U41(tt, U13(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U13(mark(z0))), MARK(U13(x1)))
   A__U41(tt, U21(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U21(mark(z0), z1)), MARK(U13(x1)))
   A__U41(tt, U22(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U22(mark(z0))), MARK(U13(x1)))
   A__U41(tt, U31(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U31(mark(z0), z1)), MARK(U13(x1)))
   A__U41(tt, U41(z0, z1, z2), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(U13(x1)))
   A__U41(tt, plus(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(U13(x1)))
   A__U41(tt, and(z0, z1), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__and(mark(z0), z1)), MARK(U13(x1)))
   A__U41(tt, isNatKind(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), a__isNatKind(z0)), MARK(U13(x1)))
   A__U41(tt, tt, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), tt), MARK(U13(x1)))
   A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1)))
   A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1)))
   A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1)))
   A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2))))
   A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1))))
   A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0))))
   A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0))))
   A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1))))
   A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0))))
   A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1))))
   A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2))))
   A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1))))
   A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1))))
   A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0))))
   A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt)))
   A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0))))
   A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0)))
   A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1)))

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
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   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
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   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
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   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
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   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
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   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
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   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
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   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
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   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
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   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
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   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
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   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)))
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   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
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   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
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   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
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   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
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   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
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   A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2))))
   A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1))))
   A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1))))
   A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0))))
   A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt)))
   A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0))))
   A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0)))
   A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
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   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
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   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
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   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
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   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
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   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
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   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
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   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
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   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
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   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
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   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1)))
   A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2)))
   A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2)))
   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)))
   A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0))))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1)))
   A__U41(tt, tt, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), tt), MARK(U13(x1)))
   A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1)))
   A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1)))
   A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1)))
   A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2))))
   A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1))))
   A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0))))
   A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0))))
   A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1))))
   A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0))))
   A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1))))
   A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2))))
   A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1))))
   A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1))))
   A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0))))
   A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt)))
   A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0))))
   A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0)))
   A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
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   MARK(and(s(z0), x1)) -> c38(MARK(s(z0)))
   A__U11(tt, plus(x0, x1), x2) -> c(A__U12(a__U11(and(a__isNatKind(x0), isNatKind(x1)), x0, x1), x2), A__ISNAT(plus(x0, x1)))
   A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1)))
   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
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   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
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   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
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   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
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   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
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   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
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   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
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   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
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   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
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   A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1))))
   A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2))))
   A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1))))
   A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1))))
   A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0))))
   A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt)))
   A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0))))
   A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0)))
   A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1)))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
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   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
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   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
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   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
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   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
   A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1))
   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
   A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
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   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
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   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
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   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
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   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
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   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
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   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
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   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
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   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
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   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
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   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1)))
   A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2)))
   A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2)))
   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)))
   A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0))))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1)))
   A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1)))
   A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1)))
   A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1)))
   A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2))))
   A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1))))
   A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0))))
   A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0))))
   A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1))))
   A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0))))
   A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1))))
   A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2))))
   A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1))))
   A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1))))
   A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0))))
   A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt)))
   A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0))))
   A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0)))
   A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(177) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, x0, U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(U21(z0, z1))) by 
   A__U41(tt, U11(z0, z1, z2), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U11(mark(z0), z1, z2)), MARK(U21(x1, x2)))
   A__U41(tt, U12(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U12(mark(z0), z1)), MARK(U21(x1, x2)))
   A__U41(tt, isNat(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__isNat(z0)), MARK(U21(x1, x2)))
   A__U41(tt, U13(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U13(mark(z0))), MARK(U21(x1, x2)))
   A__U41(tt, U21(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U21(mark(z0), z1)), MARK(U21(x1, x2)))
   A__U41(tt, U22(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U22(mark(z0))), MARK(U21(x1, x2)))
   A__U41(tt, U31(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U21(x1, x2)))
   A__U41(tt, U41(z0, z1, z2), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U21(x1, x2)))
   A__U41(tt, plus(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U21(x1, x2)))
   A__U41(tt, and(z0, z1), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__and(mark(z0), z1)), MARK(U21(x1, x2)))
   A__U41(tt, isNatKind(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), a__isNatKind(z0)), MARK(U21(x1, x2)))
   A__U41(tt, tt, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), tt), MARK(U21(x1, x2)))
   A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2)))
   A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1)))
   A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2)))
   A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2)))
   A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2)))
   A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2)))
   A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2)))
   A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2)))
   A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2)))
   A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2)))
   A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2)))
   A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2)))
   A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2)))
   A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)), MARK(U21(0, x2)))

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

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
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   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
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   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
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   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
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   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
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   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
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   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
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   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1)))
   A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2)))
   A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2)))
   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)))
   A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0))))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1)))
   A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1)))
   A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1)))
   A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1)))
   A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2))))
   A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1))))
   A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0))))
   A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0))))
   A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1))))
   A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0))))
   A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1))))
   A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2))))
   A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1))))
   A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1))))
   A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0))))
   A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt)))
   A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0))))
   A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0)))
   A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, tt, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), tt), MARK(U21(x1, x2)))
   A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2)))
   A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1)))
   A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2)))
   A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2)))
   A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2)))
   A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2)))
   A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2)))
   A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2)))
   A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2)))
   A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2)))
   A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2)))
   A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2)))
   A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2)))
   A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)), MARK(U21(0, x2)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
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   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
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   A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2)))
   A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2)))
   A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2)))
   A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2)))
   A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2)))
   A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2)))
   A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2)))
   A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2)))
   A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2)))
   A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2)))
   A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)), MARK(U21(0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
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   A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)))
   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1)))
   A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2)))
   A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2)))
   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)))
   A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0))))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1)))
   A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1)))
   A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1)))
   A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1)))
   A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2))))
   A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1))))
   A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0))))
   A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0))))
   A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1))))
   A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0))))
   A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1))))
   A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2))))
   A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1))))
   A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1))))
   A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0))))
   A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt)))
   A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0))))
   A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0)))
   A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2)))
   A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1)))
   A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2)))
   A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2)))
   A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2)))
   A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2)))
   A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2)))
   A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2)))
   A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2)))
   A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2)))
   A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2)))
   A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2)))
   A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2)))
   A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0)))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
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   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
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   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
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   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
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   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
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   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
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   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
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   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
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   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)))
   A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0))))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1)))
   A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1)))
   A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1)))
   A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1)))
   A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2))))
   A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1))))
   A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0))))
   A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0))))
   A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1))))
   A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0))))
   A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1))))
   A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2))))
   A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1))))
   A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1))))
   A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0))))
   A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt)))
   A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0))))
   A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0)))
   A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2)))
   A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1)))
   A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2)))
   A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2)))
   A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2)))
   A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2)))
   A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2)))
   A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2)))
   A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2)))
   A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2)))
   A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2)))
   A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2)))
   A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2)))
   A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(181) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, x0, U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(U22(z0))) by 
   A__U41(tt, U11(z0, z1, z2), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U11(mark(z0), z1, z2)), MARK(U22(x1)))
   A__U41(tt, U12(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U12(mark(z0), z1)), MARK(U22(x1)))
   A__U41(tt, isNat(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__isNat(z0)), MARK(U22(x1)))
   A__U41(tt, U13(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U13(mark(z0))), MARK(U22(x1)))
   A__U41(tt, U21(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U21(mark(z0), z1)), MARK(U22(x1)))
   A__U41(tt, U22(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U22(mark(z0))), MARK(U22(x1)))
   A__U41(tt, U31(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U31(mark(z0), z1)), MARK(U22(x1)))
   A__U41(tt, U41(z0, z1, z2), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(U22(x1)))
   A__U41(tt, plus(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(U22(x1)))
   A__U41(tt, and(z0, z1), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__and(mark(z0), z1)), MARK(U22(x1)))
   A__U41(tt, isNatKind(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), a__isNatKind(z0)), MARK(U22(x1)))
   A__U41(tt, tt, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), tt), MARK(U22(x1)))
   A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1)))
   A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1)))
   A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1)))
   A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2))))
   A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1))))
   A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0))))
   A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0))))
   A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1))))
   A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0))))
   A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1))))
   A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2))))
   A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1))))
   A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1))))
   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))

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

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
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   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
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   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
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   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
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   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
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   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
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   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
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   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
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   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
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   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)))
   A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0))))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1)))
   A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1)))
   A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1)))
   A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1)))
   A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2))))
   A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1))))
   A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0))))
   A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0))))
   A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1))))
   A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0))))
   A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1))))
   A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2))))
   A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1))))
   A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1))))
   A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0))))
   A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt)))
   A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0))))
   A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0)))
   A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2)))
   A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1)))
   A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2)))
   A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2)))
   A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2)))
   A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2)))
   A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2)))
   A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2)))
   A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2)))
   A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2)))
   A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2)))
   A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2)))
   A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2)))
   A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)))
   A__U41(tt, tt, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), tt), MARK(U22(x1)))
   A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1)))
   A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1)))
   A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1)))
   A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2))))
   A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1))))
   A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0))))
   A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0))))
   A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1))))
   A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0))))
   A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1))))
   A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2))))
   A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1))))
   A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1))))
   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
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   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
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   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
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   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2)))
   A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1)))
   A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2)))
   A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2)))
   A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2)))
   A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2)))
   A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2)))
   A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2)))
   A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2)))
   A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2)))
   A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2)))
   A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2)))
   A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2)))
   A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)))
   A__U41(tt, tt, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), tt), MARK(U22(x1)))
   A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1)))
   A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1)))
   A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1)))
   A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2))))
   A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1))))
   A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0))))
   A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0))))
   A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1))))
   A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0))))
   A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1))))
   A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2))))
   A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1))))
   A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1))))
   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
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   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
   A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
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   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
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   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
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   A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2)))
   A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2)))
   A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)))
   A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1)))
   A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1)))
   A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1)))
   A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2))))
   A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1))))
   A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0))))
   A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0))))
   A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1))))
   A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0))))
   A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1))))
   A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2))))
   A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1))))
   A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1))))
   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNatKind(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNatKind(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
   A__U41(tt, isNatKind(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNatKind(x0), tt) -> c12(A__PLUS(tt, a__isNatKind(x0)))
   A__U41(tt, isNatKind(x0), 0) -> c12(A__PLUS(0, a__isNatKind(x0)))
   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1)))
   A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2)))
   A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2)))
   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)))
   A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0))))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1)))
   A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1)))
   A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1)))
   A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1)))
   A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2))))
   A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1))))
   A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0))))
   A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0))))
   A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1))))
   A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0))))
   A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1))))
   A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2))))
   A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1))))
   A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1))))
   A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0))))
   A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt)))
   A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0))))
   A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0)))
   A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2)))
   A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1)))
   A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2)))
   A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2)))
   A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2)))
   A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2)))
   A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2)))
   A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2)))
   A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2)))
   A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2)))
   A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2)))
   A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2)))
   A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2)))
   A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)))
   A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1)))
   A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1)))
   A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1)))
   A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2))))
   A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1))))
   A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0))))
   A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0))))
   A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1))))
   A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0))))
   A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1))))
   A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2))))
   A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1))))
   A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1))))
   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(185) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, x0, U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) by 
   A__U41(tt, U11(z0, z1, z2), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U11(mark(z0), z1, z2)), MARK(U31(x1, x2)))
   A__U41(tt, U12(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U12(mark(z0), z1)), MARK(U31(x1, x2)))
   A__U41(tt, isNat(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__isNat(z0)), MARK(U31(x1, x2)))
   A__U41(tt, U13(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U13(mark(z0))), MARK(U31(x1, x2)))
   A__U41(tt, U21(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U21(mark(z0), z1)), MARK(U31(x1, x2)))
   A__U41(tt, U22(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U22(mark(z0))), MARK(U31(x1, x2)))
   A__U41(tt, U31(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U31(x1, x2)))
   A__U41(tt, U41(z0, z1, z2), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U31(x1, x2)))
   A__U41(tt, plus(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U31(x1, x2)))
   A__U41(tt, and(z0, z1), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__and(mark(z0), z1)), MARK(U31(x1, x2)))
   A__U41(tt, isNatKind(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), a__isNatKind(z0)), MARK(U31(x1, x2)))
   A__U41(tt, tt, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), tt), MARK(U31(x1, x2)))
   A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2)))
   A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2)))
   A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2)))
   A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2)))
   A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2)))

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

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
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   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
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   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
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   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
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   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
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   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
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   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
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   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
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   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
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   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
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   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
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   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
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   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
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   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, tt, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), tt), MARK(U31(x1, x2)))
   A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2)))
   A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2)))
   A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2)))
   A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2)))
   A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
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   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
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   A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
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   A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
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   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
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   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
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   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U21(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
   A__U41(tt, U21(x0, x1), 0) -> c12(A__PLUS(0, a__U21(mark(x0), x1)))
   A__U41(tt, U22(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNat(z0))), MARK(x1))
   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
   A__U41(tt, U31(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U31(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
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   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
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   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
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   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
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   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
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   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
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   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
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   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNat(z0), x2, x3), mark(x0)), MARK(U11(isNat(z0), x2, x3)))
   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
   A__U41(tt, x0, U11(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U11(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U11(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(0, x2, x3)) -> c12(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), s(mark(z0))), MARK(U12(x1, x2)))
   A__U41(tt, 0, U12(x1, x2)) -> c12(A__PLUS(a__U12(mark(x1), x2), 0), MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(x1, z1)) -> c12(A__PLUS(U12(mark(x1), z1), mark(x0)), MARK(U12(x1, z1)))
   A__U41(tt, x0, U12(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(U12(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U12(U12(z0, z1), x2)))
   A__U41(tt, x0, U12(isNat(z0), x2)) -> c12(A__PLUS(a__U12(a__isNat(z0), x2), mark(x0)), MARK(U12(isNat(z0), x2)))
   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
   A__U41(tt, x0, U12(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U12(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U12(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U12(plus(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U12(plus(z0, z1), x2)))
   A__U41(tt, x0, U12(and(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__and(mark(z0), z1), x2), mark(x0)), MARK(U12(and(z0, z1), x2)))
   A__U41(tt, x0, U12(isNatKind(z0), x2)) -> c12(A__PLUS(a__U12(a__isNatKind(z0), x2), mark(x0)), MARK(U12(isNatKind(z0), x2)))
   A__U41(tt, x0, U12(tt, x2)) -> c12(A__PLUS(a__U12(tt, x2), mark(x0)), MARK(U12(tt, x2)))
   A__U41(tt, x0, U12(s(z0), x2)) -> c12(A__PLUS(a__U12(s(mark(z0)), x2), mark(x0)), MARK(U12(s(z0), x2)))
   A__U41(tt, tt, U12(x1, x2)) -> c12(MARK(U12(x1, x2)))
   A__U41(tt, x0, U12(0, x2)) -> c12(A__PLUS(a__U12(0, x2), mark(x0)))
   A__U41(tt, s(z0), isNat(x1)) -> c12(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U41(tt, 0, isNat(x1)) -> c12(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U41(tt, x0, isNat(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U41(tt, x0, isNat(plus(z0, z1))) -> c12(A__PLUS(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U41(tt, x0, isNat(s(z0))) -> c12(A__PLUS(a__U21(a__isNatKind(z0), z0), mark(x0)), MARK(isNat(s(z0))))
   A__U41(tt, x0, isNat(z0)) -> c12(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, tt, isNat(x1)) -> c12(MARK(isNat(x1)))
   A__U41(tt, s(z0), U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), s(mark(z0))), MARK(U13(x1)))
   A__U41(tt, 0, U13(x1)) -> c12(A__PLUS(a__U13(mark(x1)), 0), MARK(U13(x1)))
   A__U41(tt, x0, U13(x1)) -> c12(A__PLUS(U13(mark(x1)), mark(x0)), MARK(U13(x1)))
   A__U41(tt, x0, U13(U11(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U13(U11(z0, z1, z2))))
   A__U41(tt, x0, U13(U12(z0, z1))) -> c12(A__PLUS(a__U13(a__U12(mark(z0), z1)), mark(x0)), MARK(U13(U12(z0, z1))))
   A__U41(tt, x0, U13(isNat(z0))) -> c12(A__PLUS(a__U13(a__isNat(z0)), mark(x0)), MARK(U13(isNat(z0))))
   A__U41(tt, x0, U13(U13(z0))) -> c12(A__PLUS(a__U13(a__U13(mark(z0))), mark(x0)), MARK(U13(U13(z0))))
   A__U41(tt, x0, U13(U21(z0, z1))) -> c12(A__PLUS(a__U13(a__U21(mark(z0), z1)), mark(x0)), MARK(U13(U21(z0, z1))))
   A__U41(tt, x0, U13(U22(z0))) -> c12(A__PLUS(a__U13(a__U22(mark(z0))), mark(x0)), MARK(U13(U22(z0))))
   A__U41(tt, x0, U13(U31(z0, z1))) -> c12(A__PLUS(a__U13(a__U31(mark(z0), z1)), mark(x0)), MARK(U13(U31(z0, z1))))
   A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2))))
   A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1))))
   A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1))))
   A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0))))
   A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt)))
   A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0))))
   A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0)))
   A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2)))
   A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1)))
   A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2)))
   A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2)))
   A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2)))
   A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2)))
   A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2)))
   A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2)))
   A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2)))
   A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2)))
   A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2)))
   A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2)))
   A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2)))
   A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)))
   A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1)))
   A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1)))
   A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1)))
   A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2))))
   A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1))))
   A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0))))
   A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0))))
   A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1))))
   A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0))))
   A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1))))
   A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2))))
   A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1))))
   A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1))))
   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2)))
   A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2)))
   A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2)))
   A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2)))
   A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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(189) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, x0, U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) by 
   A__U41(tt, U11(z0, z1, z2), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U41(x1, x2, x3)))
   A__U41(tt, U12(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U12(mark(z0), z1)), MARK(U41(x1, x2, x3)))
   A__U41(tt, isNat(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__isNat(z0)), MARK(U41(x1, x2, x3)))
   A__U41(tt, U13(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U13(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U41(tt, U21(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U21(mark(z0), z1)), MARK(U41(x1, x2, x3)))
   A__U41(tt, U22(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U22(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U41(tt, U31(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U31(mark(z0), z1)), MARK(U41(x1, x2, x3)))
   A__U41(tt, U41(z0, z1, z2), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__U41(mark(z0), z1, z2)), MARK(U41(x1, x2, x3)))
   A__U41(tt, plus(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U41(x1, x2, x3)))
   A__U41(tt, and(z0, z1), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__and(mark(z0), z1)), MARK(U41(x1, x2, x3)))
   A__U41(tt, isNatKind(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), a__isNatKind(z0)), MARK(U41(x1, x2, x3)))
   A__U41(tt, tt, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3)))
   A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3)))
   A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3)))
   A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3)))

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

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
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   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
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   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
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   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
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   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
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   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
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   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
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   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
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   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
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   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
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   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
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   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
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   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
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   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
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   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
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   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
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   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
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   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
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   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
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   A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2))))
   A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1))))
   A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0))))
   A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0))))
   A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1))))
   A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0))))
   A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1))))
   A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2))))
   A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1))))
   A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1))))
   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2)))
   A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2)))
   A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2)))
   A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2)))
   A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U41(tt, tt, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3)))
   A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3)))
   A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3)))
   A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
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   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
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   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
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   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
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   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
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   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
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   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
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   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
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   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
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   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
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   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
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   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
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   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
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   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
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   A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1)))
   A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1)))
   A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2))))
   A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1))))
   A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0))))
   A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0))))
   A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1))))
   A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0))))
   A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1))))
   A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2))))
   A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1))))
   A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1))))
   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2)))
   A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2)))
   A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2)))
   A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2)))
   A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U41(tt, tt, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3)))
   A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3)))
   A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3)))
   A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
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   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
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   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
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   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
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   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
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   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
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   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
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   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
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   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
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   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
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   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
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   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
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   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
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   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
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   A__U41(tt, isNatKind(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNatKind(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNatKind(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNatKind(x0)), MARK(s(z0)))
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   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
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   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
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   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
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   A__U41(tt, x0, U11(U13(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U11(U13(z0), x2, x3)))
   A__U41(tt, x0, U11(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U11(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U11(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U11(U22(z0), x2, x3)) -> c12(A__PLUS(a__U11(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U11(U22(z0), x2, x3)))
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   A__U41(tt, x0, U11(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U41(z0, z1, z2), x2, x3)))
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   A__U41(tt, x0, U11(tt, x2, x3)) -> c12(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U41(tt, x0, U11(s(z0), x2, x3)) -> c12(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U41(tt, tt, U11(x1, x2, x3)) -> c12(MARK(U11(x1, x2, x3)))
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   A__U41(tt, x0, U12(U13(z0), x2)) -> c12(A__PLUS(a__U12(a__U13(mark(z0)), x2), mark(x0)), MARK(U12(U13(z0), x2)))
   A__U41(tt, x0, U12(U21(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U12(U21(z0, z1), x2)))
   A__U41(tt, x0, U12(U22(z0), x2)) -> c12(A__PLUS(a__U12(a__U22(mark(z0)), x2), mark(x0)), MARK(U12(U22(z0), x2)))
   A__U41(tt, x0, U12(U31(z0, z1), x2)) -> c12(A__PLUS(a__U12(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U12(U31(z0, z1), x2)))
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   A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1))))
   A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1))))
   A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0))))
   A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt)))
   A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0))))
   A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0)))
   A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2)))
   A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1)))
   A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2)))
   A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2)))
   A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2)))
   A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2)))
   A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2)))
   A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2)))
   A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2)))
   A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2)))
   A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2)))
   A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2)))
   A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2)))
   A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)))
   A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1)))
   A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1)))
   A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1)))
   A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2))))
   A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1))))
   A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0))))
   A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0))))
   A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1))))
   A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0))))
   A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1))))
   A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2))))
   A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1))))
   A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1))))
   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2)))
   A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2)))
   A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2)))
   A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2)))
   A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3)))
   A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3)))
   A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
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   A__U11(tt, plus(0, x1), x2) -> c(A__U12(a__U11(a__and(tt, isNatKind(x1)), 0, x1), x2), A__ISNAT(plus(0, x1)))
   A__U11(tt, plus(plus(z0, z1), x1), x2) -> c(A__U12(a__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), x2), A__ISNAT(plus(plus(z0, z1), x1)))
   A__U11(tt, plus(s(z0), x1), x2) -> c(A__U12(a__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), x2), A__ISNAT(plus(s(z0), x1)))
   A__U11(tt, plus(z0, x1), x2) -> c(A__U12(a__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), x2), A__ISNAT(plus(z0, x1)))
   A__U11(tt, plus(z1, z2), x2) -> c(A__ISNAT(plus(z1, z2)))
   A__U11(tt, s(0), x1) -> c(A__U12(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U11(tt, s(plus(z0, z1)), x1) -> c(A__U12(a__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), x1), A__ISNAT(s(plus(z0, z1))))
   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
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   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
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   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
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   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
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   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
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   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
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   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
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   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
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   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
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   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
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   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
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   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
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   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
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   A__U41(tt, x0, U13(U41(z0, z1, z2))) -> c12(A__PLUS(a__U13(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U13(U41(z0, z1, z2))))
   A__U41(tt, x0, U13(plus(z0, z1))) -> c12(A__PLUS(a__U13(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U13(plus(z0, z1))))
   A__U41(tt, x0, U13(and(z0, z1))) -> c12(A__PLUS(a__U13(a__and(mark(z0), z1)), mark(x0)), MARK(U13(and(z0, z1))))
   A__U41(tt, x0, U13(isNatKind(z0))) -> c12(A__PLUS(a__U13(a__isNatKind(z0)), mark(x0)), MARK(U13(isNatKind(z0))))
   A__U41(tt, x0, U13(tt)) -> c12(A__PLUS(a__U13(tt), mark(x0)), MARK(U13(tt)))
   A__U41(tt, x0, U13(s(z0))) -> c12(A__PLUS(a__U13(s(mark(z0))), mark(x0)), MARK(U13(s(z0))))
   A__U41(tt, x0, U13(0)) -> c12(A__PLUS(a__U13(0), mark(x0)), MARK(U13(0)))
   A__U41(tt, x0, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, tt, U13(x1)) -> c12(MARK(U13(x1)))
   A__U41(tt, s(z0), U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), s(mark(z0))), MARK(U21(x1, x2)))
   A__U41(tt, 0, U21(x1, x2)) -> c12(A__PLUS(a__U21(mark(x1), x2), 0), MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1)))
   A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2)))
   A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2)))
   A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2)))
   A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2)))
   A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2)))
   A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2)))
   A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2)))
   A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2)))
   A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2)))
   A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2)))
   A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2)))
   A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)))
   A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1)))
   A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1)))
   A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1)))
   A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2))))
   A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1))))
   A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0))))
   A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0))))
   A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1))))
   A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0))))
   A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1))))
   A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2))))
   A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1))))
   A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1))))
   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2)))
   A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2)))
   A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2)))
   A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2)))
   A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3)))
   A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3)))
   A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(193) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, x0, plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) by 
   A__U41(tt, U11(z0, z1, z2), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U11(mark(z0), z1, z2)), MARK(plus(x1, x2)))
   A__U41(tt, U12(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U12(mark(z0), z1)), MARK(plus(x1, x2)))
   A__U41(tt, isNat(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__isNat(z0)), MARK(plus(x1, x2)))
   A__U41(tt, U13(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U13(mark(z0))), MARK(plus(x1, x2)))
   A__U41(tt, U21(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U21(mark(z0), z1)), MARK(plus(x1, x2)))
   A__U41(tt, U22(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U22(mark(z0))), MARK(plus(x1, x2)))
   A__U41(tt, U31(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U31(mark(z0), z1)), MARK(plus(x1, x2)))
   A__U41(tt, U41(z0, z1, z2), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__U41(mark(z0), z1, z2)), MARK(plus(x1, x2)))
   A__U41(tt, plus(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(plus(x1, x2)))
   A__U41(tt, and(z0, z1), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__and(mark(z0), z1)), MARK(plus(x1, x2)))
   A__U41(tt, isNatKind(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), a__isNatKind(z0)), MARK(plus(x1, x2)))
   A__U41(tt, tt, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2)))
   A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1))))
   A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0))))
   A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1))))
   A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0))))
   A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0))))
   A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2)))
   A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2)))
   A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2)))
   A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2)))
   A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2)))
   A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))

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

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
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   A__U41(tt, U31(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U31(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U31(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U31(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U31(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U31(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U31(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
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   A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2)))
   A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3)))
   A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3)))
   A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U41(tt, tt, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2)))
   A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1))))
   A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0))))
   A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1))))
   A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0))))
   A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0))))
   A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2)))
   A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2)))
   A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2)))
   A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2)))
   A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2)))
   A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
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   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
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   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
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   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
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   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
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   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
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   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
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   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
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   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
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   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
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   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
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   A__U41(tt, x0, U21(x1, z1)) -> c12(A__PLUS(U21(mark(x1), z1), mark(x0)), MARK(U21(x1, z1)))
   A__U41(tt, x0, U21(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(U12(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U21(U12(z0, z1), x2)))
   A__U41(tt, x0, U21(isNat(z0), x2)) -> c12(A__PLUS(a__U21(a__isNat(z0), x2), mark(x0)), MARK(U21(isNat(z0), x2)))
   A__U41(tt, x0, U21(U13(z0), x2)) -> c12(A__PLUS(a__U21(a__U13(mark(z0)), x2), mark(x0)), MARK(U21(U13(z0), x2)))
   A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2)))
   A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2)))
   A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2)))
   A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2)))
   A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2)))
   A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2)))
   A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2)))
   A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2)))
   A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)))
   A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1)))
   A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1)))
   A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1)))
   A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2))))
   A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1))))
   A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0))))
   A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0))))
   A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1))))
   A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0))))
   A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1))))
   A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2))))
   A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1))))
   A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1))))
   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2)))
   A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2)))
   A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2)))
   A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2)))
   A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3)))
   A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3)))
   A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U41(tt, tt, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2)))
   A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1))))
   A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0))))
   A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1))))
   A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0))))
   A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0))))
   A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2)))
   A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2)))
   A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2)))
   A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2)))
   A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2)))
   A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1))) -> c36(A__PLUS(mark(x0), a__U12(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c36(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U13(z0))) -> c36(A__PLUS(mark(x0), a__U13(mark(z0))), MARK(x0))
   MARK(plus(x0, U21(z0, z1))) -> c36(A__PLUS(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U22(z0))) -> c36(A__PLUS(mark(x0), a__U22(mark(z0))), MARK(x0))
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   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
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   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
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   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
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   A__U41(tt, U21(x0, x1), tt) -> c12(A__PLUS(tt, a__U21(mark(x0), x1)))
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   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
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   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
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   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
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   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
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   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
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   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
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   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
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   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
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   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
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   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
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   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
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   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
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   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
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   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
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   A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1))))
   A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0))))
   A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1))))
   A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0))))
   A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0))))
   A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2)))
   A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2)))
   A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2)))
   A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2)))
   A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2)))
   A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
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   A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2))))
   A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1))))
   A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1))))
   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2)))
   A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2)))
   A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2)))
   A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2)))
   A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3)))
   A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3)))
   A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1))))
   A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0))))
   A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1))))
   A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0))))
   A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0))))
   A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2)))
   A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2)))
   A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2)))
   A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2)))
   A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2)))
   A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(197) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, x0, and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) by 
   A__U41(tt, U11(z0, z1, z2), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U11(mark(z0), z1, z2)), MARK(and(x1, x2)))
   A__U41(tt, U12(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U12(mark(z0), z1)), MARK(and(x1, x2)))
   A__U41(tt, isNat(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__isNat(z0)), MARK(and(x1, x2)))
   A__U41(tt, U13(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U13(mark(z0))), MARK(and(x1, x2)))
   A__U41(tt, U21(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U21(mark(z0), z1)), MARK(and(x1, x2)))
   A__U41(tt, U22(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U22(mark(z0))), MARK(and(x1, x2)))
   A__U41(tt, U31(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U31(mark(z0), z1)), MARK(and(x1, x2)))
   A__U41(tt, U41(z0, z1, z2), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(and(x1, x2)))
   A__U41(tt, plus(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(and(x1, x2)))
   A__U41(tt, and(z0, z1), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__and(mark(z0), z1)), MARK(and(x1, x2)))
   A__U41(tt, isNatKind(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), a__isNatKind(z0)), MARK(and(x1, x2)))
   A__U41(tt, tt, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2)))
   A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2)))
   A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2)))
   A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2)))
   A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2)))
   A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2)))
   A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2)))
   A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2)))

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

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U41(U12(z0, z1), x1, x2)) -> c35(A__U41(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c35(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U13(z0), x1, x2)) -> c35(A__U41(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c35(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c35(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c35(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c35(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c35(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c35(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(tt, x1, x2)) -> c35(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c35(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c36(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
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   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
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   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
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   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
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   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
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   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U21(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U21(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U21(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U21(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U21(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U21(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U21(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U21(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U21(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U21(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1)), MARK(s(z0)))
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   A__U41(tt, U22(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U12(mark(z0), z1))), MARK(x1))
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   A__U41(tt, U22(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U22(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U22(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U22(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U22(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U22(tt), x1) -> c12(A__PLUS(mark(x1), a__U22(tt)), MARK(x1))
   A__U41(tt, U22(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U22(s(mark(z0)))), MARK(x1))
   A__U41(tt, U22(0), x1) -> c12(A__PLUS(mark(x1), a__U22(0)), MARK(x1))
   A__U41(tt, U22(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U22(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U22(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U22(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U22(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U22(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U22(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U22(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U22(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U22(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U22(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U22(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U22(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U22(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U22(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U22(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U22(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U22(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U22(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U22(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U22(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U22(mark(x0))), MARK(s(z0)))
   A__U41(tt, U22(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U22(x0), tt) -> c12(A__PLUS(tt, a__U22(mark(x0))))
   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
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   A__U41(tt, U31(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U31(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(a__U13(mark(z0)), x1)), MARK(x2))
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   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U41(tt, and(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, and(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, and(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, and(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__and(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, and(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, and(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, and(x0, x1), tt) -> c12(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U41(tt, and(x0, x1), 0) -> c12(A__PLUS(0, a__and(mark(x0), x1)))
   A__U41(tt, isNatKind(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__and(a__isNatKind(z0), isNatKind(z1))), MARK(x1))
   A__U41(tt, isNatKind(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(x1))
   A__U41(tt, isNatKind(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNatKind(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNatKind(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNatKind(x0)), MARK(isNat(z0)))
   A__U41(tt, isNatKind(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNatKind(x0)), MARK(U13(z0)))
   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNatKind(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNatKind(x0)), MARK(plus(z0, z1)))
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   A__U41(tt, isNatKind(z0), x1) -> c12(MARK(x1))
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   A__U41(tt, s(z0), U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U41(tt, 0, U11(x1, x2, x3)) -> c12(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U41(tt, x0, U11(x1, z1, z2)) -> c12(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U41(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
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   A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3)))
   A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1))))
   A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0))))
   A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1))))
   A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0))))
   A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0))))
   A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2)))
   A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2)))
   A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2)))
   A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2)))
   A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2)))
   A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2)))
   A__U41(tt, tt, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2)))
   A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2)))
   A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2)))
   A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2)))
   A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2)))
   A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2)))
   A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2)))
   A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
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   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
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   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
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   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
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   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
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   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
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   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
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   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
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   A__U41(tt, x0, U21(U21(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U21(U21(z0, z1), x2)))
   A__U41(tt, x0, U21(U22(z0), x2)) -> c12(A__PLUS(a__U21(a__U22(mark(z0)), x2), mark(x0)), MARK(U21(U22(z0), x2)))
   A__U41(tt, x0, U21(U31(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U21(U31(z0, z1), x2)))
   A__U41(tt, x0, U21(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U21(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U21(plus(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U21(plus(z0, z1), x2)))
   A__U41(tt, x0, U21(and(z0, z1), x2)) -> c12(A__PLUS(a__U21(a__and(mark(z0), z1), x2), mark(x0)), MARK(U21(and(z0, z1), x2)))
   A__U41(tt, x0, U21(isNatKind(z0), x2)) -> c12(A__PLUS(a__U21(a__isNatKind(z0), x2), mark(x0)), MARK(U21(isNatKind(z0), x2)))
   A__U41(tt, x0, U21(tt, x2)) -> c12(A__PLUS(a__U21(tt, x2), mark(x0)), MARK(U21(tt, x2)))
   A__U41(tt, x0, U21(s(z0), x2)) -> c12(A__PLUS(a__U21(s(mark(z0)), x2), mark(x0)), MARK(U21(s(z0), x2)))
   A__U41(tt, tt, U21(x1, x2)) -> c12(MARK(U21(x1, x2)))
   A__U41(tt, x0, U21(0, x2)) -> c12(A__PLUS(a__U21(0, x2), mark(x0)))
   A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1)))
   A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1)))
   A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1)))
   A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2))))
   A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1))))
   A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0))))
   A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0))))
   A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1))))
   A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0))))
   A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1))))
   A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2))))
   A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1))))
   A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1))))
   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2)))
   A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2)))
   A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2)))
   A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2)))
   A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3)))
   A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3)))
   A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1))))
   A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0))))
   A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1))))
   A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0))))
   A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0))))
   A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2)))
   A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2)))
   A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2)))
   A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2)))
   A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2)))
   A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2)))
   A__U41(tt, tt, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2)))
   A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2)))
   A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2)))
   A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2)))
   A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2)))
   A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2)))
   A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2)))
   A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U12(isNatKind(z0), x1)) -> c29(A__U12(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U12(tt, x1)) -> c29(A__U12(tt, x1))
   MARK(U12(s(z0), x1)) -> c29(MARK(s(z0)))
   MARK(U21(U11(z0, z1, z2), x1)) -> c32(A__U21(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1), x1)) -> c32(A__U21(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U21(isNat(z0), x1)) -> c32(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U13(z0), x1)) -> c32(A__U21(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c32(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c32(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c32(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c32(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1)) -> c32(A__U21(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c32(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatKind(z0), x1)) -> c32(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(tt, x1)) -> c32(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c32(MARK(s(z0)))
   MARK(U31(U11(z0, z1, z2), x1)) -> c34(A__U31(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U31(U12(z0, z1), x1)) -> c34(A__U31(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U31(isNat(z0), x1)) -> c34(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U13(z0), x1)) -> c34(A__U31(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c34(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c34(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c34(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c34(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c34(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c34(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatKind(z0), x1)) -> c34(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(tt, x1)) -> c34(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c34(MARK(s(z0)))
   MARK(U41(U11(z0, z1, z2), x1, x2)) -> c35(A__U41(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
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   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U31(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U31(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U31(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U31(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U41(tt, U41(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U41(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U41(tt, plus(x0, U11(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNat(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U41(z0, z1, z2)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U41(tt, plus(x0, plus(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U41(tt, plus(x0, and(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U41(tt, plus(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U22(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U41(tt, plus(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U41(tt, plus(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U41(tt, plus(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__isNatKind(z0), mark(x1))), MARK(x2))
   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U41(tt, plus(0, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U41(tt, plus(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1)))
   A__U41(tt, plus(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U41(tt, plus(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U13(z0)))
   A__U41(tt, plus(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1)))
   A__U41(tt, plus(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U22(z0)))
   A__U41(tt, plus(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U41(tt, plus(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U41(tt, plus(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U41(tt, plus(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__plus(mark(x0), mark(x1))), MARK(isNatKind(z0)))
   A__U41(tt, plus(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U41(tt, plus(x0, x1), x2) -> c12(MARK(x2))
   A__U41(tt, plus(x0, x1), tt) -> c12(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U41(tt, plus(x0, x1), 0) -> c12(A__PLUS(0, a__plus(mark(x0), mark(x1))))
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   A__U41(tt, and(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, and(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, and(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__U31(mark(z0), z1), x1)), MARK(x2))
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   A__U41(tt, and(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
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   A__U41(tt, and(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, and(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U41(tt, and(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, and(0, x1), x2) -> c12(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U41(tt, and(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, and(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__and(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, and(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, and(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__and(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, and(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__and(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, and(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__and(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, and(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__and(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, and(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, and(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
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   A__U41(tt, isNatKind(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNatKind(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNatKind(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNatKind(x0)), MARK(U22(z0)))
   A__U41(tt, isNatKind(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNatKind(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNatKind(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNatKind(x0)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3)))
   A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3)))
   A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1))))
   A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0))))
   A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1))))
   A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0))))
   A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0))))
   A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2)))
   A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2)))
   A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2)))
   A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2)))
   A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2)))
   A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2)))
   A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2)))
   A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2)))
   A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2)))
   A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2)))
   A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2)))
   A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2)))
   A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U41(tt, tt, and(x1, x2)) -> c12(MARK(and(x1, x2)))
   A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
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   A__U11(tt, s(s(z0)), x1) -> c(A__U12(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U11(tt, s(z0), x1) -> c(A__U12(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U11(tt, s(z1), x1) -> c(A__ISNAT(s(z1)))
   A__U41(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(U12(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNat(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNat(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(U13(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U13(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U21(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U22(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U22(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(U31(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(U41(z0, z1, z2), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U41(tt, U11(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U41(tt, U11(and(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U41(tt, U11(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U11(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U41(tt, U11(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U11(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U41(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U41(tt, U11(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U11(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U11(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U11(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U11(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U11(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U11(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U11(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U11(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U11(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U41(tt, U12(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U12(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U12(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U12(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U12(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U12(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(tt, x1)), MARK(x2))
   A__U41(tt, U12(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U12(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U12(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U12(0, x1)), MARK(x2))
   A__U41(tt, U12(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U12(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U12(mark(x0), x1)), MARK(isNat(z0)))
   A__U41(tt, U12(x0, x1), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U12(mark(x0), x1)), MARK(U13(z0)))
   A__U41(tt, U12(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U21(z0, z1)))
   A__U41(tt, U12(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U12(mark(x0), x1)), MARK(U22(z0)))
   A__U41(tt, U12(x0, x1), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U41(tt, U12(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U12(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U12(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U12(mark(x0), x1)), MARK(and(z0, z1)))
   A__U41(tt, U12(x0, x1), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U12(mark(x0), x1)), MARK(isNatKind(z0)))
   A__U41(tt, U12(x0, x1), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1)), MARK(s(z0)))
   A__U41(tt, U12(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U12(x0, x1), tt) -> c12(A__PLUS(tt, a__U12(mark(x0), x1)))
   A__U41(tt, U12(x0, x1), 0) -> c12(A__PLUS(0, a__U12(mark(x0), x1)))
   A__U41(tt, isNat(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)), MARK(x1))
   A__U41(tt, isNat(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U21(a__isNatKind(z0), z0)), MARK(x1))
   A__U41(tt, isNat(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__isNat(x0)), MARK(U11(z0, z1, z2)))
   A__U41(tt, isNat(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__isNat(x0)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U41(tt, isNat(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__isNat(x0)), MARK(U13(z0)))
   A__U41(tt, isNat(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__isNat(x0)), MARK(U21(z0, z1)))
   A__U41(tt, isNat(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__isNat(x0)), MARK(U22(z0)))
   A__U41(tt, isNat(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U41(tt, isNat(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, isNat(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U41(tt, isNat(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U41(tt, isNat(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__isNat(x0)), MARK(isNatKind(z0)))
   A__U41(tt, isNat(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U41(tt, isNat(0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c12(MARK(x1))
   A__U41(tt, isNat(x0), tt) -> c12(A__PLUS(tt, a__isNat(x0)))
   A__U41(tt, isNat(x0), 0) -> c12(A__PLUS(0, a__isNat(x0)))
   A__U41(tt, U13(U11(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U11(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(U12(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U12(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNat(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNat(z0))), MARK(x1))
   A__U41(tt, U13(U13(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U13(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U21(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U21(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U22(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U22(mark(z0)))), MARK(x1))
   A__U41(tt, U13(U31(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U31(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(U41(z0, z1, z2)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U41(tt, U13(plus(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U41(tt, U13(and(z0, z1)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__and(mark(z0), z1))), MARK(x1))
   A__U41(tt, U13(isNatKind(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(a__isNatKind(z0))), MARK(x1))
   A__U41(tt, U13(tt), x1) -> c12(A__PLUS(mark(x1), a__U13(tt)), MARK(x1))
   A__U41(tt, U13(s(z0)), x1) -> c12(A__PLUS(mark(x1), a__U13(s(mark(z0)))), MARK(x1))
   A__U41(tt, U13(0), x1) -> c12(A__PLUS(mark(x1), a__U13(0)), MARK(x1))
   A__U41(tt, U13(x0), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U11(z0, z1, z2)))
   A__U41(tt, U13(x0), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U13(mark(x0))), MARK(U12(z0, z1)))
   A__U41(tt, U13(x0), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U13(mark(x0))), MARK(isNat(z0)))
   A__U41(tt, U13(x0), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U13(mark(x0))), MARK(U13(z0)))
   A__U41(tt, U13(x0), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U13(mark(x0))), MARK(U21(z0, z1)))
   A__U41(tt, U13(x0), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U13(mark(x0))), MARK(U22(z0)))
   A__U41(tt, U13(x0), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U13(mark(x0))), MARK(U31(z0, z1)))
   A__U41(tt, U13(x0), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U13(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U41(tt, U13(x0), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U13(mark(x0))), MARK(plus(z0, z1)))
   A__U41(tt, U13(x0), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U13(mark(x0))), MARK(and(z0, z1)))
   A__U41(tt, U13(x0), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U13(mark(x0))), MARK(isNatKind(z0)))
   A__U41(tt, U13(x0), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U13(mark(x0))), MARK(s(z0)))
   A__U41(tt, U13(x0), x1) -> c12(MARK(x1))
   A__U41(tt, U13(x0), tt) -> c12(A__PLUS(tt, a__U13(mark(x0))))
   A__U41(tt, U13(x0), 0) -> c12(A__PLUS(0, a__U13(mark(x0))))
   A__U41(tt, U21(U11(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U11(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(U12(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U12(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNat(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNat(z0), x1)), MARK(x2))
   A__U41(tt, U21(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U13(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U21(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U21(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U22(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U22(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(U31(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(U41(z0, z1, z2), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U41(tt, U21(plus(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U41(tt, U21(and(z0, z1), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U41(tt, U21(isNatKind(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(a__isNatKind(z0), x1)), MARK(x2))
   A__U41(tt, U21(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(tt, x1)), MARK(x2))
   A__U41(tt, U21(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U21(s(mark(z0)), x1)), MARK(x2))
   A__U41(tt, U21(0, x1), x2) -> c12(A__PLUS(mark(x2), a__U21(0, x1)), MARK(x2))
   A__U41(tt, U21(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U21(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U21(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1)), MARK(isNat(z0)))
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   A__U41(tt, U21(x0, x1), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U21(mark(x0), x1)), MARK(U21(z0, z1)))
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   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2)))
   A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U41(tt, tt, and(x1, x2)) -> c12(MARK(and(x1, x2)))
   A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

(201) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(z0))) by 
   A__U41(tt, U11(z0, z1, z2), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__U11(mark(z0), z1, z2)), MARK(isNatKind(x1)))
   A__U41(tt, U12(z0, z1), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__U12(mark(z0), z1)), MARK(isNatKind(x1)))
   A__U41(tt, isNat(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__isNat(z0)), MARK(isNatKind(x1)))
   A__U41(tt, U13(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__U13(mark(z0))), MARK(isNatKind(x1)))
   A__U41(tt, U21(z0, z1), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__U21(mark(z0), z1)), MARK(isNatKind(x1)))
   A__U41(tt, U22(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__U22(mark(z0))), MARK(isNatKind(x1)))
   A__U41(tt, U31(z0, z1), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__U31(mark(z0), z1)), MARK(isNatKind(x1)))
   A__U41(tt, U41(z0, z1, z2), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__U41(mark(z0), z1, z2)), MARK(isNatKind(x1)))
   A__U41(tt, plus(z0, z1), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__plus(mark(z0), mark(z1))), MARK(isNatKind(x1)))
   A__U41(tt, and(z0, z1), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__and(mark(z0), z1)), MARK(isNatKind(x1)))
   A__U41(tt, isNatKind(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), a__isNatKind(z0)), MARK(isNatKind(x1)))
   A__U41(tt, tt, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), tt), MARK(isNatKind(x1)))
   A__U41(tt, s(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), s(mark(z0))), MARK(isNatKind(x1)))
   A__U41(tt, 0, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), 0), MARK(isNatKind(x1)))
   A__U41(tt, x0, isNatKind(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNatKind(0)))
   A__U41(tt, x0, isNatKind(plus(z0, z1))) -> c12(A__PLUS(a__and(a__isNatKind(z0), isNatKind(z1)), mark(x0)), MARK(isNatKind(plus(z0, z1))))
   A__U41(tt, x0, isNatKind(s(z0))) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(s(z0))))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))

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

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c28(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(and(z0, z1), x1, x2)) -> c28(A__U11(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U11(isNatKind(z0), x1, x2)) -> c28(A__U11(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U11(tt, x1, x2)) -> c28(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c28(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1)) -> c29(A__U12(a__U11(mark(z0), z1, z2), x1), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1), x1)) -> c29(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1)))
   MARK(U12(isNat(z0), x1)) -> c29(A__U12(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U12(U13(z0), x1)) -> c29(A__U12(a__U13(mark(z0)), x1), MARK(U13(z0)))
   MARK(U12(U21(z0, z1), x1)) -> c29(A__U12(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U12(U22(z0), x1)) -> c29(A__U12(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U12(U31(z0, z1), x1)) -> c29(A__U12(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U12(U41(z0, z1, z2), x1)) -> c29(A__U12(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1)) -> c29(A__U12(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U12(and(z0, z1), x1)) -> c29(A__U12(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
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   A__U41(tt, U22(x0), 0) -> c12(A__PLUS(0, a__U22(mark(x0))))
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   A__U41(tt, U31(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
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   A__U41(tt, U31(x0, x1), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U12(z0, z1)))
   A__U41(tt, U31(x0, x1), isNat(z0)) -> c12(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
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   A__U41(tt, U31(x0, x1), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U31(mark(x0), x1)), MARK(U22(z0)))
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   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U31(x0, x1), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U41(tt, U31(x0, x1), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0), x1)), MARK(and(z0, z1)))
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   A__U41(tt, U31(x0, z1), x2) -> c12(MARK(x2))
   A__U41(tt, U31(x0, x1), tt) -> c12(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U41(tt, U31(x0, x1), 0) -> c12(A__PLUS(0, a__U31(mark(x0), x1)))
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   A__U41(tt, U41(isNatKind(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__isNatKind(z0), x1, x2)), MARK(x3))
   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), isNatKind(z0)) -> c12(A__PLUS(a__isNatKind(z0), a__U41(mark(x0), x1, x2)), MARK(isNatKind(z0)))
   A__U41(tt, U41(x0, x1, x2), s(z0)) -> c12(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U41(tt, U41(x0, z1, z2), x3) -> c12(MARK(x3))
   A__U41(tt, U41(x0, x1, x2), tt) -> c12(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U41(tt, U41(x0, x1, x2), 0) -> c12(A__PLUS(0, a__U41(mark(x0), x1, x2)))
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   A__U41(tt, plus(x0, U12(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1))), MARK(x2))
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   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U21(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1))), MARK(x2))
   A__U41(tt, plus(x0, U22(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
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   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U41(tt, plus(x0, 0), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
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   A__U41(tt, plus(U13(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(a__U13(mark(z0)), mark(x1))), MARK(x2))
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   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U41(tt, plus(s(z0), x1), x2) -> c12(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
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   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2)))
   A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2)))
   A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2)))
   A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2)))
   A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3)))
   A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3)))
   A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1))))
   A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0))))
   A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1))))
   A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0))))
   A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0))))
   A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2)))
   A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2)))
   A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2)))
   A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2)))
   A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2)))
   A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2)))
   A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2)))
   A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2)))
   A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2)))
   A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2)))
   A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2)))
   A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2)))
   A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U41(tt, tt, and(x1, x2)) -> c12(MARK(and(x1, x2)))
   A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)))
   A__U41(tt, tt, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), tt), MARK(isNatKind(x1)))
   A__U41(tt, s(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), s(mark(z0))), MARK(isNatKind(x1)))
   A__U41(tt, 0, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), 0), MARK(isNatKind(x1)))
   A__U41(tt, x0, isNatKind(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNatKind(0)))
   A__U41(tt, x0, isNatKind(plus(z0, z1))) -> c12(A__PLUS(a__and(a__isNatKind(z0), isNatKind(z1)), mark(x0)), MARK(isNatKind(plus(z0, z1))))
   A__U41(tt, x0, isNatKind(s(z0))) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(s(z0))))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2)))
   A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2)))
   A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2)))
   A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2)))
   A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2)))
   A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2)))
   A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2)))
   A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2)))
   A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2)))
   A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2)))
   A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2)))
   A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U41(tt, tt, and(x1, x2)) -> c12(MARK(and(x1, x2)))
   A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)))
   A__U41(tt, tt, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), tt), MARK(isNatKind(x1)))
   A__U41(tt, s(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), s(mark(z0))), MARK(isNatKind(x1)))
   A__U41(tt, 0, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), 0), MARK(isNatKind(x1)))
   A__U41(tt, x0, isNatKind(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNatKind(0)))
   A__U41(tt, x0, isNatKind(plus(z0, z1))) -> c12(A__PLUS(a__and(a__isNatKind(z0), isNatKind(z1)), mark(x0)), MARK(isNatKind(plus(z0, z1))))
   A__U41(tt, x0, isNatKind(s(z0))) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(s(z0))))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2


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

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

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(a__isNat(z0), z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0) -> a__U13(a__isNat(z0))
   a__U12(z0, z1) -> U12(z0, z1)
   a__U13(tt) -> tt
   a__U13(z0) -> U13(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(plus(z0, z1)) -> a__and(a__isNatKind(z0), isNatKind(z1))
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__plus(z0, 0) -> a__U31(a__and(a__isNat(z0), isNatKind(z0)), z0)
   a__plus(z0, s(z1)) -> a__U41(a__and(a__and(a__isNat(z1), isNatKind(z1)), and(isNat(z0), isNatKind(z0))), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1)) -> a__U12(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U13(z0)) -> a__U13(mark(z0))
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c13(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, U13(z0), x1) -> c13(A__PLUS(mark(x1), a__U13(mark(z0))), MARK(U13(z0)))
   A__U41(tt, U21(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U41(tt, U22(z0), x1) -> c13(A__PLUS(mark(x1), a__U22(mark(z0))), MARK(U22(z0)))
   A__U41(tt, U31(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, isNatKind(z0), x1) -> c13(A__PLUS(mark(x1), a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U41(tt, s(z0), x1) -> c13(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1, z2)) -> c13(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, U12(z0, z1)) -> c13(A__PLUS(a__U12(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c13(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, U13(z0)) -> c13(A__PLUS(a__U13(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c13(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNatKind(z0)) -> c13(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c13(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c13(A__PLUS(0, mark(x0)), MARK(x0))
   A__U41(tt, 0, x1) -> c13(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c18(A__U11(a__and(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), plus(z0, z1), x1), A__AND(a__isNatKind(plus(z0, z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c18(A__U11(a__and(a__isNatKind(z0), isNatKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c18(A__U11(a__and(isNatKind(z0), isNatKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(z0))
   A__ISNAT(plus(x0, x1)) -> c18(A__AND(a__isNatKind(x0), isNatKind(x1)), A__ISNATKIND(x0))
   A__ISNAT(plus(0, x1)) -> c18(A__U11(a__and(tt, isNatKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatKind(x1)))
   A__ISNAT(s(plus(z0, z1))) -> c19(A__U21(a__and(a__isNatKind(z0), isNatKind(z1)), plus(z0, z1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNAT(s(s(z0))) -> c19(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c19(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c19(A__ISNATKIND(z0))
   A__ISNATKIND(plus(plus(z0, z1), x1)) -> c22(A__AND(a__and(a__isNatKind(z0), isNatKind(z1)), isNatKind(x1)), A__ISNATKIND(plus(z0, z1)))
   A__ISNATKIND(plus(s(z0), x1)) -> c22(A__AND(a__isNatKind(z0), isNatKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
   A__ISNATKIND(plus(z0, x1)) -> c22(A__ISNATKIND(z0))
   A__PLUS(plus(z0, z1), 0) -> c25(A__U31(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), plus(z0, z1)), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c25(A__U31(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), s(z0)), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c25(A__U31(a__and(isNat(z0), isNatKind(z0)), z0), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, 0) -> c25(A__AND(a__isNat(x0), isNatKind(x0)), A__ISNAT(x0))
   A__PLUS(0, 0) -> c25(A__U31(a__and(tt, isNatKind(0)), 0), A__AND(a__isNat(0), isNatKind(0)))
   A__PLUS(x0, s(x1)) -> c26(A__U41(a__and(and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), x1, x0), A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(plus(z0, z1))) -> c26(A__U41(a__and(a__and(a__U11(a__and(a__isNatKind(z0), isNatKind(z1)), z0, z1), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), plus(z0, z1), x0), A__AND(a__and(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(plus(z0, z1)), isNatKind(plus(z0, z1))), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c26(A__U41(a__and(a__and(a__U21(a__isNatKind(z0), z0), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), s(z0), x0), A__AND(a__and(a__isNat(s(z0)), isNatKind(s(z0))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(s(z0)), isNatKind(s(z0))), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c26(A__U41(a__and(a__and(isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), z0, x0), A__AND(a__and(a__isNat(z0), isNatKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(z0), isNatKind(z0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c26(A__AND(a__and(a__isNat(x1), isNatKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(x1), isNatKind(x1)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c26(A__U41(a__and(a__and(tt, isNatKind(0)), and(isNat(x0), isNatKind(x0))), 0, x0), A__AND(a__and(a__isNat(0), isNatKind(0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNat(0), isNatKind(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c28(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1), x1, x2)) -> c28(A__U11(a__U12(mark(z0), z1), x1, x2), MARK(U12(z0, z1)))
   MARK(U11(isNat(z0), x1, x2)) -> c28(A__U11(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U11(U13(z0), x1, x2)) -> c28(A__U11(a__U13(mark(z0)), x1, x2), MARK(U13(z0)))
   MARK(U11(U21(z0, z1), x1, x2)) -> c28(A__U11(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1, x2)) -> c28(A__U11(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U11(U31(z0, z1), x1, x2)) -> c28(A__U11(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
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   A__U41(tt, U31(x0, x1), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, U41(plus(z0, z1), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
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   A__U41(tt, U41(tt, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U41(tt, U41(s(z0), x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U41(tt, U41(0, x1, x2), x3) -> c12(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U41(tt, U41(x0, x1, x2), U11(z0, z1, z2)) -> c12(A__PLUS(a__U11(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), U12(z0, z1)) -> c12(A__PLUS(a__U12(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U12(z0, z1)))
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   A__U41(tt, U41(x0, x1, x2), U13(z0)) -> c12(A__PLUS(a__U13(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U13(z0)))
   A__U41(tt, U41(x0, x1, x2), U21(z0, z1)) -> c12(A__PLUS(a__U21(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U22(z0)) -> c12(A__PLUS(a__U22(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U22(z0)))
   A__U41(tt, U41(x0, x1, x2), U31(z0, z1)) -> c12(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c12(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, U41(x0, x1, x2), plus(z0, z1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U41(tt, U41(x0, x1, x2), and(z0, z1)) -> c12(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U41(tt, plus(x0, U13(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U13(mark(z0)))), MARK(x2))
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   A__U41(tt, plus(x0, U31(z0, z1)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
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   A__U41(tt, plus(x0, isNatKind(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), a__isNatKind(z0))), MARK(x2))
   A__U41(tt, plus(x0, tt), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U41(tt, plus(x0, s(z0)), x2) -> c12(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
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   A__U41(tt, plus(tt, x1), x2) -> c12(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
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   A__U41(tt, s(z0), U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), s(mark(z0))), MARK(U22(x1)))
   A__U41(tt, 0, U22(x1)) -> c12(A__PLUS(a__U22(mark(x1)), 0), MARK(U22(x1)))
   A__U41(tt, x0, U22(x1)) -> c12(A__PLUS(U22(mark(x1)), mark(x0)), MARK(U22(x1)))
   A__U41(tt, x0, U22(U11(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(U22(U11(z0, z1, z2))))
   A__U41(tt, x0, U22(U12(z0, z1))) -> c12(A__PLUS(a__U22(a__U12(mark(z0), z1)), mark(x0)), MARK(U22(U12(z0, z1))))
   A__U41(tt, x0, U22(isNat(z0))) -> c12(A__PLUS(a__U22(a__isNat(z0)), mark(x0)), MARK(U22(isNat(z0))))
   A__U41(tt, x0, U22(U13(z0))) -> c12(A__PLUS(a__U22(a__U13(mark(z0))), mark(x0)), MARK(U22(U13(z0))))
   A__U41(tt, x0, U22(U21(z0, z1))) -> c12(A__PLUS(a__U22(a__U21(mark(z0), z1)), mark(x0)), MARK(U22(U21(z0, z1))))
   A__U41(tt, x0, U22(U22(z0))) -> c12(A__PLUS(a__U22(a__U22(mark(z0))), mark(x0)), MARK(U22(U22(z0))))
   A__U41(tt, x0, U22(U31(z0, z1))) -> c12(A__PLUS(a__U22(a__U31(mark(z0), z1)), mark(x0)), MARK(U22(U31(z0, z1))))
   A__U41(tt, x0, U22(U41(z0, z1, z2))) -> c12(A__PLUS(a__U22(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U22(U41(z0, z1, z2))))
   A__U41(tt, x0, U22(plus(z0, z1))) -> c12(A__PLUS(a__U22(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U22(plus(z0, z1))))
   A__U41(tt, x0, U22(and(z0, z1))) -> c12(A__PLUS(a__U22(a__and(mark(z0), z1)), mark(x0)), MARK(U22(and(z0, z1))))
   A__U41(tt, x0, U22(isNatKind(z0))) -> c12(A__PLUS(a__U22(a__isNatKind(z0)), mark(x0)), MARK(U22(isNatKind(z0))))
   A__U41(tt, x0, U22(tt)) -> c12(A__PLUS(a__U22(tt), mark(x0)), MARK(U22(tt)))
   A__U41(tt, x0, U22(s(z0))) -> c12(A__PLUS(a__U22(s(mark(z0))), mark(x0)), MARK(U22(s(z0))))
   A__U41(tt, x0, U22(0)) -> c12(A__PLUS(a__U22(0), mark(x0)), MARK(U22(0)))
   A__U41(tt, x0, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, tt, U22(x1)) -> c12(MARK(U22(x1)))
   A__U41(tt, s(z0), U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U41(tt, 0, U31(x1, x2)) -> c12(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(x1, z1)) -> c12(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U41(tt, x0, U31(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(U12(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U12(mark(z0), z1), x2), mark(x0)), MARK(U31(U12(z0, z1), x2)))
   A__U41(tt, x0, U31(isNat(z0), x2)) -> c12(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U41(tt, x0, U31(U13(z0), x2)) -> c12(A__PLUS(a__U31(a__U13(mark(z0)), x2), mark(x0)), MARK(U31(U13(z0), x2)))
   A__U41(tt, x0, U31(U21(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U21(mark(z0), z1), x2), mark(x0)), MARK(U31(U21(z0, z1), x2)))
   A__U41(tt, x0, U31(U22(z0), x2)) -> c12(A__PLUS(a__U31(a__U22(mark(z0)), x2), mark(x0)), MARK(U31(U22(z0), x2)))
   A__U41(tt, x0, U31(U31(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U41(tt, x0, U31(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, U31(plus(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U41(tt, x0, U31(and(z0, z1), x2)) -> c12(A__PLUS(a__U31(a__and(mark(z0), z1), x2), mark(x0)), MARK(U31(and(z0, z1), x2)))
   A__U41(tt, x0, U31(isNatKind(z0), x2)) -> c12(A__PLUS(a__U31(a__isNatKind(z0), x2), mark(x0)), MARK(U31(isNatKind(z0), x2)))
   A__U41(tt, x0, U31(tt, x2)) -> c12(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U41(tt, x0, U31(s(z0), x2)) -> c12(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U41(tt, tt, U31(x1, x2)) -> c12(MARK(U31(x1, x2)))
   A__U41(tt, x0, U31(0, x2)) -> c12(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U41(tt, s(z0), U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U41(tt, 0, U41(x1, x2, x3)) -> c12(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(x1, z1, z2)) -> c12(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U41(tt, x0, U41(U11(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U11(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(U12(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U12(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U12(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNat(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U41(tt, x0, U41(U13(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U13(mark(z0)), x2, x3), mark(x0)), MARK(U41(U13(z0), x2, x3)))
   A__U41(tt, x0, U41(U21(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U21(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U21(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U22(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__U22(mark(z0)), x2, x3), mark(x0)), MARK(U41(U22(z0), x2, x3)))
   A__U41(tt, x0, U41(U31(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c12(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U41(tt, x0, U41(plus(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(and(z0, z1), x2, x3)) -> c12(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U41(tt, x0, U41(isNatKind(z0), x2, x3)) -> c12(A__PLUS(a__U41(a__isNatKind(z0), x2, x3), mark(x0)), MARK(U41(isNatKind(z0), x2, x3)))
   A__U41(tt, x0, U41(tt, x2, x3)) -> c12(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U41(tt, x0, U41(s(z0), x2, x3)) -> c12(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U41(tt, tt, U41(x1, x2, x3)) -> c12(MARK(U41(x1, x2, x3)))
   A__U41(tt, x0, U41(0, x2, x3)) -> c12(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U41(tt, s(z0), plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U41(tt, 0, plus(x1, x2)) -> c12(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, x2)) -> c12(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U41(tt, x0, plus(x1, U11(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, U12(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1)), mark(x0)), MARK(plus(x1, U12(z0, z1))))
   A__U41(tt, x0, plus(x1, isNat(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U41(tt, x0, plus(x1, U13(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U13(mark(z0))), mark(x0)), MARK(plus(x1, U13(z0))))
   A__U41(tt, x0, plus(x1, U21(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1)), mark(x0)), MARK(plus(x1, U21(z0, z1))))
   A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0))))
   A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0))))
   A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2)))
   A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2)))
   A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2)))
   A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2)))
   A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2)))
   A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2)))
   A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2)))
   A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2)))
   A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2)))
   A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2)))
   A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2)))
   A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2)))
   A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U41(tt, tt, and(x1, x2)) -> c12(MARK(and(x1, x2)))
   A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)))
   A__U41(tt, s(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), s(mark(z0))), MARK(isNatKind(x1)))
   A__U41(tt, 0, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), 0), MARK(isNatKind(x1)))
   A__U41(tt, x0, isNatKind(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNatKind(0)))
   A__U41(tt, x0, isNatKind(plus(z0, z1))) -> c12(A__PLUS(a__and(a__isNatKind(z0), isNatKind(z1)), mark(x0)), MARK(isNatKind(plus(z0, z1))))
   A__U41(tt, x0, isNatKind(s(z0))) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(s(z0))))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, tt, isNatKind(x1)) -> c12(MARK(isNatKind(x1)))
S tuples:
   A__U31(tt, z0) -> c10(MARK(z0))
   A__AND(tt, z0) -> c15(MARK(z0))
   A__ISNATKIND(s(z0)) -> c23(A__ISNATKIND(z0))
   MARK(isNat(z0)) -> c30(A__ISNAT(z0))
   MARK(isNatKind(z0)) -> c39(A__ISNATKIND(z0))
   MARK(s(z0)) -> c41(MARK(z0))
   A__U12(tt, z0) -> c2(A__ISNAT(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   MARK(U13(z0)) -> c31(MARK(z0))
   MARK(U22(z0)) -> c33(MARK(z0))
   A__U11(tt, 0, x1) -> c(A__U12(tt, x1))
   A__U11(tt, z0, x1) -> c(A__ISNAT(z0))
   A__U41(tt, s(z0), x1) -> c12(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c12(A__PLUS(mark(x1), 0), MARK(x1))
   A__U41(tt, x0, s(z0)) -> c12(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, tt, x1) -> c12(MARK(x1))
   A__U41(tt, x0, tt) -> c12(A__PLUS(tt, mark(x0)))
   A__U41(tt, x0, 0) -> c12(A__PLUS(0, mark(x0)))
   A__U41(tt, U11(z0, z1, z2), x1) -> c13(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U41(tt, U12(z0, z1), x1) -> c13(A__PLUS(mark(x1), a__U12(mark(z0), z1)), MARK(U12(z0, z1)))
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   A__U41(tt, x0, U21(z0, z1)) -> c13(A__PLUS(a__U21(mark(z0), z1), mark(x0)), MARK(x0))
   A__U41(tt, x0, U22(z0)) -> c13(A__PLUS(a__U22(mark(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0, z1)) -> c13(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U41(tt, x0, s(z0)) -> c13(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
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   A__ISNATKIND(plus(0, x1)) -> c22(A__AND(tt, isNatKind(x1)))
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   A__U41(tt, x0, plus(x1, U22(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__U22(mark(z0))), mark(x0)), MARK(plus(x1, U22(z0))))
   A__U41(tt, x0, plus(x1, U31(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U41(tt, x0, plus(x1, U41(z0, z1, z2))) -> c12(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U41(tt, x0, plus(x1, plus(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U41(tt, x0, plus(x1, and(z0, z1))) -> c12(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U41(tt, x0, plus(x1, isNatKind(z0))) -> c12(A__PLUS(a__plus(mark(x1), a__isNatKind(z0)), mark(x0)), MARK(plus(x1, isNatKind(z0))))
   A__U41(tt, x0, plus(x1, tt)) -> c12(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U41(tt, x0, plus(x1, s(z0))) -> c12(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U41(tt, x0, plus(x1, 0)) -> c12(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U41(tt, x0, plus(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(U12(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U12(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1), x2)))
   A__U41(tt, x0, plus(isNat(z0), x2)) -> c12(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U41(tt, x0, plus(U13(z0), x2)) -> c12(A__PLUS(a__plus(a__U13(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U13(z0), x2)))
   A__U41(tt, x0, plus(U21(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U21(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1), x2)))
   A__U41(tt, x0, plus(U22(z0), x2)) -> c12(A__PLUS(a__plus(a__U22(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U22(z0), x2)))
   A__U41(tt, x0, plus(U31(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U41(tt, x0, plus(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(and(z0, z1), x2)) -> c12(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U41(tt, x0, plus(isNatKind(z0), x2)) -> c12(A__PLUS(a__plus(a__isNatKind(z0), mark(x2)), mark(x0)), MARK(plus(isNatKind(z0), x2)))
   A__U41(tt, x0, plus(tt, x2)) -> c12(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c12(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U41(tt, x0, plus(0, x2)) -> c12(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U41(tt, tt, plus(x1, x2)) -> c12(MARK(plus(x1, x2)))
   A__U41(tt, s(z0), and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U41(tt, 0, and(x1, x2)) -> c12(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U41(tt, x0, and(x1, z1)) -> c12(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U41(tt, x0, and(U11(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U11(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U11(z0, z1, z2), x2)))
   A__U41(tt, x0, and(U12(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U12(mark(z0), z1), x2), mark(x0)), MARK(and(U12(z0, z1), x2)))
   A__U41(tt, x0, and(isNat(z0), x2)) -> c12(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U41(tt, x0, and(U13(z0), x2)) -> c12(A__PLUS(a__and(a__U13(mark(z0)), x2), mark(x0)), MARK(and(U13(z0), x2)))
   A__U41(tt, x0, and(U21(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U21(mark(z0), z1), x2), mark(x0)), MARK(and(U21(z0, z1), x2)))
   A__U41(tt, x0, and(U22(z0), x2)) -> c12(A__PLUS(a__and(a__U22(mark(z0)), x2), mark(x0)), MARK(and(U22(z0), x2)))
   A__U41(tt, x0, and(U31(z0, z1), x2)) -> c12(A__PLUS(a__and(a__U31(mark(z0), z1), x2), mark(x0)), MARK(and(U31(z0, z1), x2)))
   A__U41(tt, x0, and(U41(z0, z1, z2), x2)) -> c12(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U41(tt, x0, and(plus(z0, z1), x2)) -> c12(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U41(tt, x0, and(and(z0, z1), x2)) -> c12(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U41(tt, x0, and(isNatKind(z0), x2)) -> c12(A__PLUS(a__and(a__isNatKind(z0), x2), mark(x0)), MARK(and(isNatKind(z0), x2)))
   A__U41(tt, x0, and(tt, x2)) -> c12(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U41(tt, x0, and(s(z0), x2)) -> c12(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U41(tt, tt, and(x1, x2)) -> c12(MARK(and(x1, x2)))
   A__U41(tt, x0, and(0, x2)) -> c12(A__PLUS(a__and(0, x2), mark(x0)))
   A__U41(tt, s(z0), isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), s(mark(z0))), MARK(isNatKind(x1)))
   A__U41(tt, 0, isNatKind(x1)) -> c12(A__PLUS(a__isNatKind(x1), 0), MARK(isNatKind(x1)))
   A__U41(tt, x0, isNatKind(0)) -> c12(A__PLUS(tt, mark(x0)), MARK(isNatKind(0)))
   A__U41(tt, x0, isNatKind(plus(z0, z1))) -> c12(A__PLUS(a__and(a__isNatKind(z0), isNatKind(z1)), mark(x0)), MARK(isNatKind(plus(z0, z1))))
   A__U41(tt, x0, isNatKind(s(z0))) -> c12(A__PLUS(a__isNatKind(z0), mark(x0)), MARK(isNatKind(s(z0))))
   A__U41(tt, x0, isNatKind(z0)) -> c12(A__PLUS(isNatKind(z0), mark(x0)), MARK(isNatKind(z0)))
   A__U41(tt, tt, isNatKind(x1)) -> c12(MARK(isNatKind(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_2, a__U13_1, a__U21_2, a__U22_1, a__U31_2, a__U41_3, a__and_2, a__isNat_1, a__isNatKind_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__AND_2, A__ISNATKIND_1, MARK_1, A__U12_2, A__U21_2, A__U11_3, A__U41_3, A__ISNAT_1, A__PLUS_2

Compound Symbols:   c10_1, c15_1, c23_1, c30_1, c39_1, c41_1, c2_1, c6_1, c31_1, c33_1, c_1, c12_2, c12_1, c13_2, c13_1, c18_3, c18_2, c19_2, c19_1, c22_2, c22_1, c25_3, c25_2, c26_4, c26_3, c28_2, c28_1, c29_2, c29_1, c32_2, c32_1, c34_2, c34_1, c35_2, c35_1, c36_2, c36_1, c37_2, c37_1, c38_2, c38_1, c_2